I have been working for about 15 years on a genealogy the families and descendants of each of the main Beckwith immigrants to the US. I would love to have information on your line from W.S.A. Beckworth of Appling Co. GA. I have him on census records, but not much else.
My belief, contrary to what most southern Beckwiths/Beckworths believe, is that there is no difference in the names. Lots of the CT Beckwiths used -ith and -orth interchangeably. Also, if you say Beckwith with a very southern accent, you get Beckwuth,or as many would hear it, Beckworth.
This is my opinion for what it's worth (or is that with?).
Sorry for the late answer to your query. I had pneumonia in Fev. and then suffered through the end of May coaching Jr. High and High School track teams. The fatigue factor was extremely high. I am now catching up on over 200 e-mails.
I would like to know more aboout your line of descent from W.A.S. Beckworth.