A not too reliable article, but says this about Pop Goes the Weasel.
"The tune was published in "Gow's Repository," issued in four volumes between 1799 and 1820."
The article also mentions the 1850 Miller and Beecham printing (see Masato, above) as the earliest found, British printings somewhat later- 1854. But several of the Bodleian printings are undated.
See: http://www.worldwidewords.org/qa/qa-pop1.htm: Pop Goes the Weasel

Duke University has a version of "Pop Goes The Weasel" dated 1855, New York, which has many of the lines of the version posted by Naemanson. In Historic American Sheet Music: Pop Goes the Weasel