In response to Brian Peters two questions, looking through the seven versions (of which two have only one verse so only five are relevant) in "Cecil Sharp's Collection of Engllish Folk Songs" edited by Maud Karpeles...

1)
One version is from Mrs Overd, sung 22 August 1904. It has the "Look how my love's swimming along" verse as given in Bronson.

In none of the five relevant versions does she "tumble" and "taver"

However,..
"totter" and "tumber" appear in the Elizabeth Mogg version
"taver" appears in the Louie Hooper version
"totters" and "tremble" appear in the Jane Guilford version
"rollin'" and "tumblin'" appear in the W.Spearing version

But only Mrs. Overd's version has "which makes my heart quaver" or anything like it. None of the other four indicate that he is fearful. Contrite, perhaps, what with wanting to go after her with a small boat and/or provide her a coffin (in some versions one could think he hopes to prevent her death after all; in others it seems he simply wants to retrieve the bodies)

2)
None of these five refer to ill-fortune suffered by the ship. In Louie Hooper's version he "was troubled / with her and her baby". In some she asks to be thrown overboard. In some she asks to be sent or taken back home. Conceivably those requests (or her misery and complaining that those requests may represent) could have angered him.

On the other hand, perhaps the idea that the ship would be in trouble due to the woman and her baby and her malfeasance was so well understood it did not need to be included in the song. (In my reading, HE was as culpable as SHE, but I've just been reminded by reading "Albion's Seed" of how deeply double the double standard was in these matters.)