Pop here means to pawn. The song is about spending all your money on boozing. So: 'Up and down the City Road' which runs between the Angel Islington and Old Street in London, 'In and out of the Eagle' a pub still to be found on the corner of City Road and Shepherdess Walk, 'That's the way the money goes' spending all your hard-earned on drinking, 'Pop goes the weasle' you pawn your weasle. Probably not referring to a rodent here, the best guess anyone's come up with is the a weasle was a slang term for a tailor's iron. So, you hawk the tools of your trade to get another pint...Easily done.