Oops - I forgot to add that one of the trees I checked gives a death date and place for Thaddeus that fits with him moving to Michigan:
Thaddeus Cutler Gilbert born 21 Jul 1781 in Brookfield, Worcester, Massachusetts died 21 November 1848 in Jackson, Jackson, Michigan — Age: 67
No source is noted (McMurtrie/Parkinson family tree).
More below from an online tree (again, all this unsourced stuff has to be checked and followed up):
Asa Gilbert b. 26 May 1750, Brookfield, Worcester Co., MA, m. Hannah Barnes (dau. of Thomas and Mary (Howe) Barnes), b. 24 Aug 1740, Brookfield, Worcester Co., MA, d. 1796, St. Johnsbury, VT. Asa died aft. 1806, prob. in Pittsfield, Ruland Co., VT. They had: Arunah Gilbert Sally Gilbert Lucy Gilbert Asa Gilbert <---this brother moved to Michigan Thaddeus Gilbert <----- presumably "your" Thaddeus Sophia Gilbert
One source noted for early ancestors in above tree is "The Gilbert Family: Descendents of Thomas Gilbert, 1582(?)-1659" by Homer Worthington Brainard, Harold Simeon Gilbert and Clarence Almon Torrey.