You need to get a copy of "Beckwith Notes" by A.C. and E.S. Beckwith published from 1899 to 1906. Book is available form Higginson Books in MA. Your line is delat with in the book. Information is mostly trustworthy (unlike Paul Beckwith's "The Beckwiths".)
Your Beckwiths are descendants of Matthew Beckwith of CT. The Centre County Beckworths are apparently descendants of the MD Beckwiths.