I researched everything backwards from my Greatgrandmother, on RootsWeb.
My Greatgrandmother was Marilla Briggs (b. 1852). Her Father was Abel Briggs (b. 1823). His Father was William Briggs (b. 1783 in RI; d. Jan 15, 1860) He is buried in Independence Cemetery, Allegany County, NY. His son, Johnson was born in CT.The other children were born in Independence, NY
I wasn't able to find an Eliza as daughter of William.