This one is a real puzzle. My gg-grandmother was a Wells and goes back to these lines. My husband is a Fitzrandolph descendant. I am a Doty, Curtis and Martin descendant. Both of us are Freeman and Miner descendants. You can guess how tangled my research is on the subject! I finally stopped looking at anything to do with the Wells/Welles family much before 1700 until I can get sorted out.
Here's one source of our difficulties: the Gustav Anjou fraudulent genealogies. Some time ago, I ran into the info totally by accident, just by googling the terms "Doty family" and "genealogy".
He lived 1863-1942, and people would hire him to research their families. He knew they wanted connections to important people, so he created them, based around real gaps and brick walls in the actual lines. He quoted nonexistent documents to back up his claims, knowing that his clients would never try to verify his research. Poof! Now you're descended from kings!
Many professional genealogists are aware of him and avoid his reports or anything unsourced which might be contaminated by his materials, but most of us amateurs are a little naive about accepting stuff from online... (and offline, for that matter). Not that the internet has been bad for genealogists, just that it perpetuates the bad with the good.
If you want to see a list of the materials that Anjou published, go to http://personal.linkline.com/xymox/fraud/fraud.htm
and click on the "Fraudulent Lineages" link. It is a site by the Sons & Daughters of America's First Families (not sure of their antecedents but the site is useful and seems to be clean and safe).
The site contains 1. a set of hallmarks by which you can identify Anjou's handiwork if it isn't identified by author name, and 2. a list of fraudulent genealogies known to be published by Anjou. Unfortunately the list is quite long (Anjou claimed to have published 192 by 1927, and he lived another 15 years) and the Weld/Wells/Welles/Willis/Wilds family is one of them. Most of the families are early New England families, so anyone with roots back that far in the U.S. is likely to run into some of his smoke and mirrors.
Sorry to be a downer, but I'm guessing the Welles problem was based on one of his deceptions. Otherwise, my husband would probably be the Emperor of the Holy Roman Empire (descended from Charlemagne, don't you know!) AND King of England (through the Welles, though I expect I could give him a run for his money there, since I'm descended from that line through more of my ancestors than he is! Alas!) today.
I'm thinking about going to an LDS family history reading room and requesting his Welles genealogy just so I know what he did say, so I can find out where the really hinky stuff is and avoid it!