I'm pleased to say I have found the following relating to your branch of the Kilby family:
Arthur Eustace KILBY was born 19 August 1877 at 7 Denmark Place, Twickenham Common, Twickenham (source Birth Certificate)
He was the son of Charles William KILBY, Tinman (this is a Tinsmith or Tinker) and Annie Elizabeth KILBY (nee NAZER)
Charles William KILBY married Annie Elizabeth NAZERbetween Sept and Dec 1871 (PRO reference DEC 1871 Brentford 3a 136) (source PRO index)
Charles William KILBY was born 2 December 1848 at Hanworth Road, Twickenham (source Birth Certificate)
He was the son of William KILBY, Police Constable and Eliza KILBY (nee HOWARD)
Annie Elizabeth NAZER was born between June and September 1850 (PRO reference SEP 1850 Brentford III 36) (source PRO index)
She was the daughter of John W NAZER , Labourer and Sarah (?) (source 1851 Census)
John Willocks NAZER was baptised at St Peter's, Sandwich Kent on 9 April 1815. He was the son of John Gill NAZER and Ann (?) (source IGI)
John Gill NAZER was born on 19 January 1788. He was baptised at St Peter's, Sandwich Kent on 6 February 1788. He was the son of John NAZER and Elizabeth BURVILL (source IGI)
From the 1881 CENSUS: Dwelling: 14 Bedford Rd Census Place: Twickenham, Middlesex, England Source: FHL Film 1341326PRO Ref RG11Piece 1343Folio 56Page 36 Marr Age Sex Birthplace Charles W. KILBY M 32M Twickenham, Middlesex, England Rel: Head Occ: General Labourer Anne KILBY M 30F Twickenham, Middlesex, England Rel: Wife William J. KILBY U 8M Twickenham, Middlesex, England Rel: Son Occ: Scholar Arthur E. KILBY U 3M Twickenham, Middlesex, England Rel: Son Occ: Scholar Charlotte NAZER U 25F Twickenham, Middlesex, England Rel: Sister Occ: Stewardess
As you can see Arthur Eustace had at least 1 brother (William J) born in 1872/3 and Ann's sister Charlotte was visiting/lodging. Both Bedford Road and Denmark Road are still in existence and run parallel to each other near Strawberry Hill. Unfortunately, I could not find this KILBY family in the 1851 census but I did find the NAZER'S near by:
From the 1851 CENSUS:
135 2nd Cross Road, Twickenham John W NAZER M 36Sandwich, Kent Rel: Head Occ: Labourer Sarah NAZER M 33Burham(?), Kent Rel: Wife Occ: Chairwoman (same as Charlady - cleaner) James D NAZER U 10 Deptford, Kent Rel: Son John R NAZER U 8 Twickenham, Middlesex Rel: Son William S NAZER U 5 Twickenham, Middlesex Rel: Son George NAZER U 3 Twickenham, Middlesex Rel: Son Ann E NAZER U 8months Twickenham, Middlesex Rel: Daughter
I think there is a lot more scope to research both the KILBYs and the NAZERs. Trying to find William and Elizabeths marriage record would be the next step, plus a more detailed look at the Brentford/Twickenham Census for 1841 - 1871.
If you let me know your postal address I can send you the documentation I have.