The full first verse of the rhyme is:
Half a pound of twopenny rice, (pronounced tuppeny)
Half a pound of treacle.
Mix it up and make it nice,
Pop! goes the weasel.
And the most often used second verse is:
Up and down the City Road, (a busy London street)
In and out the Eagle, (a famous landmark pub)
That’s the way the money goes
Pop! goes the weasel.
As a born and bred cockney I can state with authority that this phrase originated in the East End of London, England, where to “pop” something was (and is) slang terminology (as stated by Cecil) meaning to pawn it.
Poverty was at one point pretty abject in the East End and many men were working on piece work, only employed as and when work was available, (when, for instance, a ship docked). The wives had to eke out the wages to feed the often large family and when there were no wages they would pawn the husband’s “best” suit, using the money to buy cheap but filling ingredients (two penny rice).
The reference to “weasel” is a corruption of “whistle”, which is itself a shortening of the Cockney rhyming slang term, “whistle and flute” - or suit.
So to pop the weasel meant to pawn the husband’s suit.
References to cobblers and mulberry bushes appear to have come about sometime in the late 1800’s, after the rhyme crossed the Atlantic to America and are not part of the original rhyme.
Welcome to the Straight Dope Message Boards, goonerkif, we’re glad you found us. For future ref: when you start a thread, it’s helpful to other readers to provide a link to the column in question. Saves search time and helps keep us on the same page. No biggie, you gave the column title and the date, so I’ve just added the link. You’ll know for next time. And, as I say, welcome!
As a kid (in England, 50 some years ago)) I knew the same verses that goonerkif quotes, both about spending money, apparently by wife and husband, on food and booze respectively. My mother used to sing them to me. She was not a cockney, but she did grow up in a working class (or lower middle class, which was more her) area of London (Finsbury Park). I do not recall ever hearing any other verses: nothing about cobbler’s benches, let alone mulberry bushes (which, as Cecil rightly says, belong to a quite different song). I agree that it is about spending money, and then having to pawn something.
I also remember hearing somewhere, a long time ago (not from my mother, maybe on British TV or radio), that popping the weasel meant pawning one’s pocket watch. I can’t provide a source for that, though, and I have no idea why “weasel” might be slang for a watch.
On the other hand, it could well be about pawning your coat. Weasel does appear to be authentic rhyming slang for coat: weasel and stoat - coat.