1871 : in Middlesborough age 23 (he's a lodger in a household)
1881: in Middlesborough age 33, with wife & children
1891: in Middlesborough age 42, with wife & children
1901: in Middlesborough age 52, with children
Note: in 1891, his youngest child there is named Barbara.
Barnard Castle comes under the Teesdale Registration District.
Search GRO BIRTHS:https://www.gro.gov.uk/groWAITE, born 1847 +/-2yrs registered Teesdale
Only one John WAITE in range : Dec Qtr 1847.
No mms listed - indicating he was illegitimate, ie: there is likely no father listed on cert, only an unmarried mother.
CENSUS 1851: Thorngate, in Township of Barnard Castle
HO107 -Piece 2387/ Folio 445 /Pg49
Head: Barbara WEAITE 32, unm, Dressmaker, b Depdale, Yorkshire
Son: John WEAITE 3, b B'd Castle
MARRIAGE 1851: Dec Qtr 1851, Teesdale
Thomas BRUNSKILL
Barbara WAITE
BIRTH 1852: GRO - March Qtr 1852 Teesdale
Elizabeth BRUNSKILL, mms WAITE
CENSUS 1861: Thorngate, in Township of Barnard Castle
RG 9- Piece 3719/ Folio 79/Pg42
Head: Barbara BRUNSKILL 41, widow, Washwoman, b Depdale, Yorkshire
Son: John BRUNSKILL 14, Joiner, b B'd Castle
Dau: Elizabeth BRUNSKILL 9, Scholar, b B'd Castle
Barbara's marriage may have been very brief, if this death - in the same quarter in which she married - is her husband:
DEATH 1851: GRO - Dec Qtr 1851 Teesdale
Thomas BRUNSKILL, age 44
If John named his father on his 1872 marriage as Thomas WAITE, it is more than likely he cobbled together his mother's name WAITE under which he was registered born, with the first name of Thomas BRUNSKILL. The latter may or may not have been his natural father!
Cheers
AMBLY