When I Was Noo But Sweet Sixteen in the DT is Jeannie Robertson's set (perhaps as recorded by Jean Redpath?); somehow I missed it when I posted a transcription from Jeannie's singing in the thread in Jeff's third link, along with the lyric as modified by the Black family.  The set in Jeff's second link is a collated one; three verses from Jeannie again, with one verse (the second) taken from a late 18th century chapbook and changed a bit to fit the tune, which is not Jeannie's and was itself collated from two versions, in the Caledonian Pocket Companion (c. 1735) and the Caledonian Museum.  The collation was made by Stephen Sedley (who never knew when to leave well alone!), and published in his book The Seeds of Love (1967), which is where I got those details.

The site Jeri found is, unfortunately, riddled with inaccuracies; sources are not given, modern songs are not credited to their authors and, as usual, a good proportion of the "Irish" songs are really Scottish or English.  The text quoted is, I think, from the Dubliners, who also seem to have learned the song from Jeannie (as did almost everybody who sings it), but have unaccountably changed the song into the third person; perhaps they felt uncomfortable singing a song from a woman's perspective.  Traditional versions of this Scottish song are always sung in the first person.  That said, I think you've got the goods there, Jeri.  I have a feeling that someone posted that text here a while ago, but the search engine isn't finding it; perhaps it was too recently to have been indexed yet.