Michelle, it appears that you and I are 9th cousins 1x removed. (That means that you and my mother are 9th cousins, and me and your kids are 10th cousins.)
The only ancestor we share is the original Jonas Weed. Your first Jonas Jr (b. 1647) was younger brother to my John (b. 1643).
Much of what I know about these relatives has been provided by Jack Weed, a cousin somewhere down the line who has gathered it all into a book. (But it only follows the descendants of John, so it wouldn't help you beyond the original Jonas's children.) You may have seen him around these boards.
I have added your information to my tree (which is how I was able to measure our relation).