You have given me some more things to research. I couldn't find a Sturbridge, NH, only Sturbridge, Mass. I do have a copy of Vital Records of Sturbridge, Massachusetts, to the year 1850, that has the birth records of Jesse spelled Jase, son of John and Rebeckah Blunt. It also has his siblings Andrew, Anna, John, and John. The marriage of John and Rebecca (spelling varied).
In the 1790 census for New Hampshire, in Plainfield Town lists Jesse and his brother Andrew. It states that there are three people besides Jesse living in the household.

Rome Vital Records from 1776-1843 lists that Jesse and Diadma were married on June 12, 1788. It lists the following children: Franklin at Winthrop, Maine..Jan. 26, 1795, Cynthia at New Sharon, Maine..Feb. 15,1798, Eunice in New Sharon July 22, 1800, and Philina in New Sharon April 8, 180?.
Do you know when your Mary was born?

I have never been able to find a last name for Diadma/Diadami. It makes sense that she would have been related some how. They stuck together so much back then. Jesse's grandfather married his cousin Naomi Lovejoy (her mother was Bathsheba Blunt)