I'm not sure! I don't have a lot on them. My dad has more, but I'm not sure what he has. So far, I have that Anna's father's name was Frederick, her mother's name was Mary, and her siblings were Frederick, Katherine, and Caroline. Do any of those ring a bell? In the 1880 census (from Geddes, NY. Onondaga Co.): Frederick Sr. is 59, Mary is 45, Frederick Jr. is 18, Katherine, 9, and Caroline, 7. After that date, I see no sign of any of them! Not sure if they moved out of state...or even out of the country! It also says that Frederick Sr. and Jr. worked in the salt mines.
It looks like the actual spelling, at least according to the census, was "Begle". I don't know if that's correct or if the census taker was just spelling it phonetically.
I believe I've seen your g-g grandfather in the census, as well, on one of my searches.