I just found out on ancestry.ca that the same Mary Sykes (who married John Barker in 1811) was the daughter of Abel Sykes and Susannah Beaver (according to several trees).
As of now, I'll list Abel and Susannah as "uncertain" parents of Mary Sykes, since I couldn't find any census records mentioning all three of them (yet). Although I am planning to continue researching about the Sykes, feel free to give me assistance.