About Walter Plummer
So far the only evidence for this person's existence is his persistent appearance in various family trees.
To be a "prominent merchant" and a Knight, he would have to have been born a minimum of ten years earlier than 1616 - which makes the 1590 date sound more plausible - and/or to have lived well past 1639, in which case he probably wasn't the man who emigrated to Bermuda and died there.
There seem to have been several William, Walter and Thomas Plummers active at approximately the same time, making it difficult to sort out which one is which.
There certainly was a Sir Walter Plummer in England, ft. c. 1660s, who was defrauded by one Robert Wright, later Chief Justice of the King’s Bench (1687–89). Wright, as a young wastrel, bailed himself out of debt by mortgaging his estate to Sir Walter, falsely claiming it to be free of financial encumbrances. (How Wright wriggled out of that one is unknown.) But that Sir Walter either never went to Bermuda, or didn't stay there.