None of Huntington's words seem to be older than the 1850s. His suggestion that the song dates back to the 18th century in America is speculation.
There may have been an old dance melody that was used for "Pop Goes the Weasel," but so far nothing firm.

1st verse: Dance introduced in that form in 1854.
2nd. verse: The cobbler of the English song replaced by "around the mulberry bush."
3rd Verse: "Go draw two lines..." Describes the dance introduced by Queen Victoria.
4th verse: "John Bull sends forth his iron hounds..." About the fight over the fishing grounds off the east coast (1850s, I believe). Several songs about this fight. Here are some verses from two of them, taken from American Memory, Nineteenth Century Song sheets.

The Fishery Fight Down East
(Tune- There was an old chap of the West Countrie).
1. There's a row away down in the East Countrie,
A breach of a treaty, the English have found;
'Tis all about fishing upon the salt sea,
And catching of Codfish upon British ground.
Cho: Right too ral, looral, tooral-luddity, etc.
3. So about this same quarrel we want our old "Dan"
To expound us the treaty etc.


The Other Side of Jordan (Minstrel song, 1860, H. de Marsan, Publisher)
Oh, de Codfish Question, it made a mighty talk,
'Twas a subject dat we nebber said a word on,
But when John Bull got sassy, de Yankees made him walk,
And day drobe him to the oder side of Jordan.

Dere's Poor Uncle Tom. and de Old Folks at Home, etc.

5th verse: He tells us in a pious hum,
How we abuses Uncle Tom, etc.
Obviously written after the appearance of the book, "Uncle Tom's Cabin."

6th verse: A penny for a spool of thread- found in British broadsides of the 1850s.