Hi Emily,
I think you have made a mistake with the marriage of Wiliam b.1851. The
marriage evidence you have attached is from a census in Wales, where
it shows him as married with son William Walter, however if you look at
his place of birth, it says South Newton, which bears no relation to
William Francis Adams born in Backwell to Thomas Adams and Ann
(Parrett). If you look at my Hibbs/Adams/Dyte tree which is public, there
is a marriage record attached showing him marrying Louisa Merrick. He
is living in Chelvey at the time, which is close to his father (same farm
area). He lives in Chelvey / Backwell/ Brockley area right up to 1911
census with Louisa.
So, to summarise -l think you either have the wrong parents for your
Willam, if it's the correct marriage, or the wrong marriage if it's definitely
Thomas and Ann's son you are trying to find, whichever way you are
researching.
The marriage certificate you have for Francis William and Margaret
Annie shows him as 21 in 1881 when he got married, which also doesn't
agree with his birth in 1851/2 - he would be 30. This appears to be
someone not linked to William Francis Thomas in my tree.