Hi Carole,
My great-grandfather Samuel Snook was the son of Anna Bates and Samuel Snook. Anna's father was Francis Bates, the son of Stephen Bates Jr. and the grandson of Stephen Bates Sr. It is more than likely that Stephen Sr's first wife was a Baker. The Bates family had several generations of Baptists (the Roger Williams style Baptists from Rhode Island--there are some accounts that Stephen Sr. was a Baptist minister (and several Francis Bates' grandfathers before him were active in the church because they were recorded as conducting marriages) but I have never gotten primary source affirmation of this (Stephen's actual confirmation as a minister). Re: Bakers--check records in N. Kingstowne, RI, Pownal, VT, and other towns in NY such as around Cooperstown.
I'll check out your family tree. Thanks for contacting me and let's keep in touch.
Best wishes,
Howard Snooks