Hi Mike, so nice to hear back from you. Yes I was born and live in the US. After doing some of my family genealogy I decided to do some work on my wife's family since she had some interesting rumors about "coming over on the Mayflower" and "soldiers in the American Revolution" with your King George. I thought the Mayflower story was crazy but after doing research found that they did not come on the famous "Mayflower" of 1620. They are one of a very few passengers that were listed with the "Winthrop Fleet" that had a "Mayflower" ship in 1630, it is possible. To us Americans that is concidered "Ancient History". It is for my family, that I am doing the research. Bear in mind, I am not referring to any member of the Atherton in this paragraph, please do not interpret it that way. Just a little background.
Now on th the Atherton's. I have not really had much of an original thought on this subject, but have managed to compile forty pages or more of notes from various sources.
books.google.com was my main source for information from Lancashire...I have read a lot, I get stuck reading all of this history of that area that I was familiar with, but did not such know details.
So, doing a search on "Pers Atherton" will bring up the procedings of "RALPH ATHERTON versus THOMAS ATHERTON, re DISPUTED TITLE TO MESSUAGES AND LANDS IN SUTTON, RAINFORD, AND WHISTON. To the King our Sovereign Lord." from "THE RECORD SOCIETY FOR THE publication of Original Documents RELATING TO LANCASHIRE AND CHESHIRE. VOLUME XXXII." There are a few other sources listed.
Searching "Thomas Atherton of Bickerstafle" will bring up "A History of the Chantries Within the County Palatine of Lancaster By Francis Robert Raines" with some more history of Thomas Atherton.
After reading it can all be a little confusing and definitely takes multiple readings and creating charts...and somtimes the information appears to be contradictary.
I think I have read other information that I will look up and try to send about this. I appreciate your expertise, along with the other researchers.