I tried to research this from the possible father's end, but can't find a way to prove the family relations.
I did find some interesting stuff about Champlin Babcock (b. 1757) and added that to his profile: https://www.wikitree.com/wiki/Babcock-135
Most interesting was that he was a Corporal in Rhode Island's Black regiment. All officers were white, so Champlin was white for sure, but he worked with the black privates at least in 1778.
Also found him in the Tinmouth Vt. Census in 1790. Tinmouth was were a bunch of Rhode Island Seventh Day Baptists relocated around that time. This Champlin Babcock family just left so few records. I put what is thought to be true in the "Research Note" section....just can't prove it. It is thought to be true that this was Champlin Jr.'s father and that the family moved through VT living in Danby and Wallingford as well as Tinmouth. Thought that Champlin Jr. had siblings Samuel and George....and I did find what looks like that same sibling group at Otto NY later on as heads of household.