There is a Henry Squire buried at Middlebury Cemetery on Newton. St. You may want to look at the nearby gravestones or the church records (the plot was owned by Deacon Titus Chapman, and I imagine the church may have some records about who is interred there).
There are pictures of all the gravestones up on my facebook firstname.lastname@example.org. The cemetery is usually locked and you may have to jump the fence. (try the back corner.. )