There are many Burrills in Massachusetts. Do you have dates for your gggrandfather? There are a number of Josephs. Who were your Joseph's children?
I am related to John Burrill, who is a descendant of John Alden and Priscilla Mullins, who came in the Mayflower.
Here is my line:
John Alden and Priscilla Mullens Joseph Alden and Mary Simmons Mercy Alden and John Burrill John Burrill and Mary Humphrey John Burrill and Anna Vinton Anna Burrill and Samuel Nevers Mary Nevers and Samuel Kearney Francis O'Neal Kearny and Eleanor Nelson Hannah Kearney and Trueman Hathaway Kearn Samuel David Kearn and Rhoda Viola Branch Living Living
Among my Burrill records are at least six Josephs, with birthyears of 1719, 1747, 1761, 1811, 1794, and 1836. Hope this helps, Tom