This is a long thread and there seem to be others running on same family so not sure if you've got this.
There doesn't seem to be a William (stone mason) with a son also called William born abt 1860/1 in Manchester, so maybe the Manchester is right (especially if your uncle stayed with relatives there), but perhaps William senior never existed.
The 1861 census has a William Wilson 1 year old the son of Mary Wilson age 24 unmarried cotton winder both born Manchester, living in Todmorden, Lancs
Piece 3237, Folio 75, page 19
The 1871 has a Wm Wilson age 11 born Manchester as a pupil at the Bluecoat school Newton with Scales. Don't know if it's the same boy of course, but the school was a charity school, taking poor children.
Piece 4219, Folio 22, page 4
He may have been told that his father was dead and also called William and grew up believing it, or invented a father and a profession so as not to leave a blank on the marriage cert.
Maybe Mary married had more children and the Manchester relatives were William's half siblings.