In The Winthrop Fleet, Anderson's write-up on Robert Weldon adds no new information beyond his earlier sketch in The Great Migration Begins (pp. 1964-5), repeating it almost word-for-word. As to the issue Cheryl is focusing on, Anderson concludes that Weldon migrated and settled in Charlestown in 1630.
Does that make him part of the Winthrop Fleet? In the75 page preliminary section and 50 page Introduction (by far the most important and useful part of the new book, in my view), Anderson deals at length with that question. He summarizes the scope of The Winthrop Fleet as follows: "this volume attempts to include all those immigrants who came with the Winthrop Fleet in 1630, as well as those 1629 arrivals who were associated with the 1629 planning activities of the Massachusetts Bay Company. We have not attempted to compile a simple list, such as that prepared by Banks. However, one could compile such a list by taking note of those sketches in this volume with a 1630 year of migration." (p. xvii)
So, if we want WT to specially label immigrants as "came with the Winthrop Fleet", the PGM team could adopt Anderson's criteria as our rule, and the profiles included in that book with a 1630 date of immigration as our "list."
Sorry for the longish answer to Cheryl's well-phrased and brief question.