You know from 1871 census that William was born St Johns Chapel, approx 1837. You know from his marriage cert that his father was William, a coal miner. So this is probably him and his family.
Marriage 9 April 1836, St. Johns Chapel, Stanhope. William Hodgson, bachelor, and Susan Greggs, spinster. Witnesses : Featherston Hodgson and Mary Greggs.
Baptism 21 June 1837, St Johns Chapel, Stanhope. William Hodgson, son of William (a Miner) and Susan Hodgson of Fair Hills.
1841, Iveston, Lanchester,
Wm Hodgin, 25, Labourer, Y,
Susan Hodgin, 20, Y,
Wm Hodgin, 3, Y,
Featherston Hodgin, 1, Y,
HO107/301/14/6/7
1851, Tow Law, Wolsingham,
William Hodgson, 36, Coal Miner, b. Stanhope,
Susan Hodgson, wife, 32, b. Stanhope,
William Hodgson, son, 13, Coal Putter, b. Stanhope,
Featherston Hodgson, son, 11, Iron Stone Putter, b. Stanhope,
Thomas Hodgson, son, 10m, b. Wolsingham.
HO107/2388/470/2
1861, Tow Law, Wolsingham,
William Hodgson, 46, Coal Miner, b. Stanhope,
Susan Hodgson, wife, 42, b. Stanhope,
RG9/3728/39/30
1871, Tow Law, Wolsingham,
William Hodgson, 56, Coal Miner, b. Stanhope,
Susannah Hodgson, wife, 52, b. Stanhope,
RG10/4953/53/25
This is probably William jnr in 1861, has a daughter Mary A. as per 1871. Williams brother Featherston Hodgson is living on the same street, on the next census page.
1861, Cornforth Lane, Cornforth,
William Hodgson, 23, Coal Miner, b. Weardale,
Jane Hodgson, 21, b. Yorks, Rippon,
Mary A. Hodgson, 1, dau, b. Cassop,
RG 9/3697/19/34
There is a marriage of a William Hodgson and Jane Johnson, Jun qtr 1859, Auckland, (marriage confirmed on Durham Registrars site). Looks like the only marriage of a William Hodgson to a Jane in the right time frame.
Hate to put a dampener on things though, but William is unlikely to be your John Henry Hodgson father if his name was not on the birth cert.
There is a death in Stockton in Mar qtr 1878 of a William Hodgson, age 39. Its the only one of around the right age at around the right time. His burial is on the free index on Durham Records Online, abode - the County Asylum. Its pay per view, the full burial record may have more details.
Alan.