Tamsin,
As I'm sure you know, this is clearly a member of the "Tobacco is an Indian
Weed" family, which has loads of references in the Roud Index as no. 1457.
The earliest I can find is Thomas d'Urfey's "Pills to Purge Melancholy",
vol. 3, pp.291-292, published 1719-1720. I wouldn't be surprised if the song
goes back to the previous (17th) century, but I don't know about the 16th.
Hope this helps.
Simon
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