@ Robert B. Waltz: "It is almost certain that no one, in the Weller Brothers period, would have named a ship the 'Billy of Tea,' because the name wouldn't mean anything. Of course the ship's name could have changed in oral tradition, but its use in a song about the Wellers is an anachronism."

And not a deliberate joke?

Reading the rest of this thread, I wonder... Can I really be (almost) the only one who suspects that this song (poem?) was never meant to be entirely factual, but a deliberately humorous parody, with its shore-based whalers experiencing an impossible "Nantucket sleigh ride" and a ship with a name that means "pot of tea"?

I find it hard to imagine that the author was uniquely lacking in a sense of humor.