So I had to have a look.
And there’s a few theories, the coat theory, but the others are pretty interesting too:
There has been much speculation about the meaning of the phrase and song title, “Pop Goes the Weasel”.[1][6] Some say a weasel is a tailor’s flat iron, silver-plate dishes, a dead animal, a hatter’s tool, or a spinner’s weasel.[1][23][17] One writer notes, “Weasels do pop their heads up when disturbed and it is quite plausible that this was the source of the name of the dance.”[1]