This is the family in 1881:
Norton
Address Given Name Surname Relationship to Head Marital Status Age Estimated Birth Year Gender Occupation Birth City Birth County Birth Country
Game Keeper Cottage William Stephens Head Married 34 1847 Male Game Keeper Swindon Gloucestershire England
Game Keeper Cottage Martha Stephens Wife Married 32 1849 Female Wife Childswickham Gloucestershire England
Game Keeper Cottage Frd. George Stephens Son 14 1867 Male Scholar Stanton Gloucestershire England
Game Keeper Cottage Ellen Maria Stephens Daughter 9 1872 Female Scholor Rudford Gloucestershire England
Game Keeper Cottage Chorles R. Stephens Son 7 1874 Male Scholor Rudford (Churcham) Gloucestershire England
Game Keeper Cottage Albert J. Stephens Son 5 1876 Male Scholor Churcham Gloucestershire England
Game Keeper Cottage Eliza J. Stephens Daughter 2 1879 Female Malvern Wells Worcestershire England
Game Keeper Cottage Emily Stephens Daughter Female Norton (Wells) Gloucestershire

1891
Norton
Name Relationship Gender Age Birth Year Birth Place Civil parish Ecclesiastical parish Residence Place Registration district Sub registration district ED, Institution or Vessel Piece Folio
William Stephens Head Male 44 1847 Swindon Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Martha Stephens Wife Female 42 1849 Childs Wickham Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Albert J Stephens Son Male 15 1876 Churcham Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Eliza Stephens Daughter Female 12 1879 Malvern Wells Worcestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Emily Stephens Daughter Female 10 1881 Norton Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Agnes Stephens Daughter Female 8 1883 Norton Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Alice Stephens Daughter Female 6 1885 Norton Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Laura E Stephens Daughter Female 4 1887 Norton Gloucestershire England Norton Norton Norton Gloucestershire England Kingsholm 4 2010 58
Arthur W Stephens Son Male 1 1890 Norton Gloucestershire England Norton Norton Norton Gloucestershire England

1901
Keepers Cottage, Norton
Household Number Name Relation to Head Age Estimated Birth Year Gender Birth Place
16 William Stephen Head 54 1847 Male Swindon, Gloucestershire, England
16 Martha Stephen Wife 52 1849 Female Childs Wickham
16 William Stephen Son 11 1890 Male Norton, Gloucestershire, England
16 Laura Stephen Daughter 13 1888 Female Norton
16 Francis Stephen Daughter 9 1892 Female Norton
16 Charles Blakeney Grandson 3 1898 Male Gloucestershire, England

1911
Name Relation to Head Birth Date Age Gender Marital Status Years Married Occupation Birth Place Address
William Stephens Head 1847 64 Male Married 44 Woodman Swindon, Gloucestershire Tythe House, Norton, Gloucestershire
Martha Stephens Wife 1849 62 Female Married 44 Child Wickham, Gloucestershire Tythe House, Norton, Gloucestershire

The 1911 Census tells us that William and Martha were married 44 years and GRO Birth Index tells us that Martha's maiden name is WOOD. This leads us to this marriage:

Marriages Jun 1866
STEPHENS William Winchcomb 6a 707
Wood Martha Winchcomb 6a 707

Details sourced from Ancestry:
Name: William Stephens
Gender: Male
Marriage Age: 20
Event Type: Marriage
Birth Year: abt 1846
Marriage Date: 26 May 1866
Marriage Place: Didbrook cum Hailes, Gloucestershire, England
Parish as it Appears: Didbrook
Spouse: Martha Wood Aged 18
Residence: Rye field
Father of William Stephens: Deceased
Father of Martha Wood: James Wood, Labourer.
Witnesses: George Hughes and Eliza Hughes.

Both William and Martha are buried at Norton:
Year: 1924
Month: May
Day: 8
Surname: STEPHENS
Forenames: William
Residence: Tythe Barn Cottages Norton Norton
Age_at_death: 79
Officiating_Minister: H M Ward
Event: Burial
Cause_of_death:
Memoranda:
Notes:
Register_Reference: P232 IN 1/8
Page_No: 97
Parish_Chapel: Norton

Year: 1928
Month: Oct
Day: 6
Surname: STEPHENS
Forenames: Martha
Residence: 9 Cross Keys Lane Gloucester
Age_at_death: 80
Officiating_Minister: W A Longdon Vicar
Event: Burial
Cause_of_death:
Memoranda:
Notes:
Register_Reference: P232 IN 1/8
Page_No: 100
Parish_Chapel: Norton

Mike

The entry marked N(to) K(nown) could be son William. It is noted that he is not with parents in any Census.

1851 Census
House Number Given Name Surname Relationship Age Estimated Birth Year Gender Birth Place
20 William Barnes Head 64 1787 Male Castle Moreton, Worcestershire, England
20 Sarah Barnes Wife 45 1806 Female Berkeley, Gloucestershire, England
20 Charles Barnes Son 9 1842 Male Newent, Gloucestershire, England
20 Benjamin Barnes Son 7 1844 Male Newent, Gloucestershire, England
20 Henry Barnes Son 3 1848 Male Newent, Gloucestershire, England

1861 Census
Newent
Household Number Given Name Surname Relationship Age Estimated Birth Year Gender Birth City Birth County Birth Country
128 Sarah Barnes Head 60 1801 Female Berkeley Gloucestershire England
128 Thomas Barnes Son 32 1829 Male Newent Gloucestershire England
128 Charles Barnes Son 20 1841 Male Newent Gloucestershire England

1871 Census:
Newent
Household schedule number Given Name Surname Relationship Age Estimated Birth Year Gender Birth City Birth County Birth Country
42 Mary Taysill Head 84 1787 Female Newent Gloucestershire England
42 Sarah Barnes Lodger 74 1797 Female Newent Gloucestershire England

1881 Census:
Staunton Near Newent
Address Given Name Surname Relationship to Head Marital Status Age Estimated Birth Year Gender Occupation Birth City Birth County Birth Country
The Moat Edward Boulter Head Widower 50 1831 Male Ag Lab Newent Gloucestershire England
The Moat Sarah Barnes Lodger Widow 80 1801 Female Stone Gloucestershire England
The Moat Charles Wilks Lodger 50 1831 Male Ag Lab Redmarley Worcestershire England

William died between 1851 and 1861. This is his burial:
Year: 1857
Month: Mar
Day: 10
Surname: BARNES
Forenames: William
Residence: Newent
Age_at_death: 76
Officiating_Minister: G. J. Gill
Event: Burial
Cause_of_death: [not sta
Memoranda:
Notes:
Register_Reference: P225 IN 1 / 13
Page_No: 108
Parish_Chapel: Newent

and Sarah died after 1881 and this is her burial:
Year: 1888
Month: Apr
Day: 20
Surname: BARNES
Forenames: Sarah
Residence: Newent Union Workhouse
Age_at_death: 87
Officiating_Minister: T.Hayes
Event: Burial
Cause_of_death:
Memoranda:
Notes:
Register_Reference: P309 in 1/8
Page_No: 78
Parish_Chapel: Staunton near Newent

The 1851 Census gives William's place of birth as Castlemorton, Worcestershire and we find this baptism on familysearch.org. We should add that we do not have sufficient evidence to be certain:

Name: William Barns
Gender: Male
Christening Date: 29 Jan 1786
Christening Date (Original): 29 JAN 1786
Christening Place: CASTLEMORTON,WORCESTER,ENGLAND
Father's Name: Willm. Wagstaff
Mother's Name: Anne Barns

There is more than one baptism for a Sarah Lewis in Stone around 1800.

Mike

and they are in Derby at time of 1911 Census:
Name Relation to Head Birth Date Age Gender Marital Status Occupation Birth Place Address
Arthur Barnes Head 1871 40 Male Married Watch & Clock Maker Gloucester, England 59 Peet St Derby
Emily Barnes Wife 1881 30 Female Married Norton, Gloucester, England 59 Peet St Derby
Arthur Barnes Son 1905 6 Male Birmingham, Worcester, England 59 Peet St Derby
John Barnes Son 1908 3 Male Sutton Coldfield, Warwickshire, England 59 Peet St Derby

Age given at time of marriage suggest Arthur is born c1871 and Emily c1881.
This would appear to be Baptism for Emily:
Year: 1881
Month: Mar
Day: 6
Parents_Surname: STEPHENS
Child_Forenames: Emily
Fathers_Forenames: William
Mothers_Forenames: Martha
Mothers_Surname:
Residence: Norton
Occupation: Keeper
Officiating_Minister: F E Broome Witts Vicar
Event: Baptism
Memoranda:
Notes:
Register_Reference: P232 IN 1/8
Page_Number: 10
Parish_Chapel: Norton

and for Arthur:
Year: 1870
Month: Jun
Day: 26
Parents_Surname: BARNES
Child_Forenames: Arthur
Fathers_Forenames: William
Mothers_Forenames: Marianne
Mothers_Surname:
Residence: Kingsholme
Occupation: Tailor
Officiating_Minister: Thomas Turner.Vicar of Norton
Event: Baptism
Memoranda:
Notes:
Register_Reference: P232 IN 1/6
Page_Number: 95
Parish_Chapel: Norton

The GRO Index tells us that his mother's maiden name is Clarke and this would be the parent's marriage:
Groom Surname Groom Forename Bride Surname Bride Forename District Parish Building Year Register Entry
BARNES William CLARK Mary Ann Gloucester Northgate St John the Baptist 1864 55 No 3 58

Here is the family in 1871 and 1881:
1871 Census
Household schedule number Given Name Surname Relationship Age Estimated Birth Year Gender Birth City Birth County Birth Country
269 William Barnes Head 41 1830 Male Taynton Gloucestershire England
269 Mary A Barnes Wife 27 1844 Female Skenfrith Monmouthshire Wales
269 James Barnes Son 6 1865 Male St Mary De Crypt Gloucester Gloucestershire England
269 William Barnes Son 5 1866 Male St Catherine Gloucestershire England
269 Arthur Barnes Son 1 1870 Male St Catherine Gloucestershire England

1881 Census
Address Given Name Surname Relationship to Head Marital Status Age Estimated Birth Year Gender Occupation Birth City Birth County Birth Country
9 Vine Terrace William Barnes Head Married 50 1831 Male Journeyman Tailor Newent Gloucestershire England
9 Vine Terrace Mary Barnes Wife Married 39 1842 Female ((Junior Cl)) Skenfrith Monmouth Wales
9 Vine Terrace James Barnes Son 16 1865 Male Junior Clerk Gloster Gloucestershire England
9 Vine Terrace William Barnes Son 15 1866 Male Scholar Gloster Gloucestershire England
9 Vine Terrace Arthur Barnes Son 10 1871 Male Scholar Gloster Gloucestershire England
9 Vine Terrace Albert E. Barnes Son 6 1875 Male Scholar Gloster Gloucestershire England
9 Vine Terrace John H. Barnes Son 1 1880 Male Gloster Gloucestershire England

Taking the BARNES line back further was not straightforward but we find this marriage:
Year: 1827
Month: Oct
Day: 25
Grooms_Surname: BARNES
Grooms_Forenames: William
Grooms_Age:
Groom_Condition: [not stated]
Grooms_Occupation:
Grooms_Residence: Newent
Grooms_Fathers_Surname:
Grooms_Fathers_Forenames:
Grooms_Fathers_Occupation:
Brides_Surname: LEWIS
Brides_Forenames: Sarah
Brides_Age:
Brides_Condition: [not stated]
Brides_Occupation:
Brides_Residence: of this parish
Brides_Fathers_Surname:
Brides_Fathers_Forenames:
Brides_Fathers_Occupation:
Licence_or_Banns: Banns
Date_of_Banns:
Signature_or_Mark: Both mark
Witness_1: Paul Barnard
Witness_2: Hannah Barnard
Other_Witnesses:
Officiating_Minister: Wm Bushell Curate
Event: Marriage
Memoranda:
Notes:
Register_Reference: P326 IN 1/8
Page_Number: 12
Parish_Chapel: Taynton

and this baptism:
Year: 1827
Month: Oct
Day: 25
Parents_Surname: LEWIS
Child_Forenames: William
Fathers_Forenames: [not stated]
Mothers_Forenames: Sarah
Mothers_Surname:
Residence: Tainton
Occupation: Domestic Servant
Officiating_Minister: W[illia]m Bushell
Event: Baptism
Memoranda: illegitimate
Notes:
Register_Reference: P326 IN 1/5
Page_Number: 27
Parish_Chapel: Taynton

Note William's baptism took place on the same day as the marriage of his parents.

It was the 1861 Census entry for William which provided the clue:
Household Number Given Name Surname Relationship Age Estimated Birth Year Gender Birth City Birth County Birth Country
185 William Barnes Head 31 1830 Male Taynton Gloucestershire England
185 Henry Barnes Lodger 13 1848 Male Newent Gloucestershire England

The maiden name of Henry's mother is Lewis and baptisms of siblings can be found on this website.

Mike

Gr 1911 Census, 3 Bath Cottages, Apperley , nr Tewkesbury

William BARNES, Head, 63, Married, General labourer, b. Glos, Deerhurst
Mary Ann, Wife, 64, Married,Glos, Deerhurst
Francis, Son, 32, Unmarried, Basket Maker, Glos, Deerhurst
May COULDREY, Gdaur, 11, Glos, Churchdown

41 years married.
5 children born alive, 1 died.
4 rooms in the house.

GR 1881 Census, Cottage, Apperley

William BARNES, Head, Mar, 33, Gardener, b. Gloucestershire, Apperley
Mary Ann, Wife, Mar, 34, Gloucestershire, Deerhurst
Mary Ann, Daur, 10, Gloucestershire, Deerhurst
Arthur, Son, 8, Gloucestershire, Deerhurst
George T, Son, 6, Gloucestershire, Deerhurst
Annie M, Daur, 3, Gloucestershire, Deerhurst
Francis J, Son, 2, Gloucestershire, Deerhurst

Possible marriage,

GR England & Wales marriages 1837-2008
First Name William
Last Name Barnes
Gender Male
Year 1870
Spouse
Image Quarter 2
Country England
County Gloucestershire
District Tewkesbury
District Number
Registry Number
Volume 6A
Page 805
Line Number 235
Entry Number

William Barnes married one of the people below:

Mary Ann MARGRETT
Caroline BLOXHAM

However, the entry from Glos BMD Births marks him as Arthur William rather than Arthur Clark.

BARNES , Arthur William, Mother’s former name, MARGRETT,
1872 Cheltenham, Tewkesbury, Deerhurst 10 136

GR England & Wales marriages 1837-2008
First Name Arthur
Last Name Barnes
Gender Male
Year 1902
Spouse
Image Quarter 1
Country England
County Gloucestershire
District Gloucester
District Number
Registry Number
Volume 6A
Page 537
Line Number 81
Entry Number
Category Births, Marriages & Deaths
Record set England & Wales Marriages 1837-2005
Collections from Great Britain, England
Spouse Match Spouse Match: Arthur BARNES married Emily STEPHENS
First Name Emily
Last Name Stephens
Gender Female
Year 1902
Spouse
Image Quarter 1
Country England
County Gloucestershire
District Gloucester
District Number
Registry Number
Volume 6A
Page 537
Line Number 336