Thank you for telling me about Balyis, Bolisbavas, Baliukas. I had never found "BOLI" in the few books, or websites; thought it perhaps a nickname. (Seems Americans like to, or used to give nicknames to people, i.e,. John could be called Jack.)
When I visited a Lithuanian church here, in Shenandoah, Pennsylvania, I found a number of Konstantin's children's birth & baptismal records. There, too, were a few records for Vincent Vabolis, Joseph Vabolis & Teofila Vabolis, but I have not encountered them in the US Census records...maybe the pages are too faded anymore.
I don't know if Konstantin & his wife named their children after other family members (their parents, grandparents, etc.). Their names were Anna (1893-1988), Sophia (1896-1924), Albert (1897-1915), Emilia (1898-?), Bronislaea (1900-1997), Mary Helen (1903-1989), Agatha/Agnes (1905- ), Helene (1907- ), Edward (1908-1992), & twins Veronica (1915- ) & Francis (1915- ). Four are still living, but age has taken its toll on their memories.
There was an Albert Vabolis who came to Pennsylvania between 1900-1910, but I have not been able to learn if he might have been related to my Konstantin.
It seems that there are very few paper trails for me to try to follow up. I appreciate your help, your comments. Even Konstantin's birth date is still really a question: each Census indicated a different age, even his death certificate...I have estimated 1864, though I could be very wrong. He did die in Jan., 1940.