The three verses by Tony from Darwin (and in slightly different form by M. Ted) are the best known, certainly the one learned by children. In the same website that mentions "Gow's Repository," (see link above) Michael Quinion gives the "usual British version" (also common in America except for the City road-Eagle verse). They are in part Tony's-

Half a pound of tuppenny rice,
Half a pound of treacle,
That's where the money goes,
Pop goes the weasel.

Up and down the City road,
In and out the Eagle,
That's the way the money goes,
Pop goes the weasel.

Every night when I go out
The Monkey's on the table.
Take a stick and knock it off,
Pop goes the weasel.

A penny for a ball of thread,
Another for a needle,
That's the way the money goes,
Pop goes the weasel.

All around the cobbler's bench
The monkey chased the people;
The donkey thought 'twas all in fun,
Pop goes the weasel.
These "nursery" rhymes all seem to be post-1850, or after the dance was introduced. Any evidence of their prior existence??
Perhaps a verse like this was the start (also from Quinion):

Queen Victoria's very sick,
Prince Albert's got the measles.
The children have the whooping cough,
And pop! Goes the weasel.

He found this in the March, 1860 issue of the "Southern Literary Messenger" of Richmond, VA.

A David Joyce (also quoted in Quinion) says the "tune is a version of one used for the country dance, "The Haymakers," which has the same form as "Strip the Willow" and "Bab at the Bowster," dances in which a bridge is formed. Anyone know anything about these?

Here is the website again: Pop Goes the Weasel