You say in an earlier post that you have the details of William Wilson's marriage.Marriage certificate hopefully.
Is a father for William mentioned on there? Or left blank?
The fact that William was living with his grandparents, makes me think Mr Teather was not his father.
My great great grandmother M.C ,had an illegitimate daughter,my gt grandmother, who lived with M.Cs parents as their child. M.C married the following year, and named her second child the same as her illegitimate one! My gt grandmother married naming her grandfather as father on her marriage certificate.