FWIW :
One of the many recordings of this song and its variants now on YouTube, mentions that Tannahill: "apparently adapted it from a song written by John Hamilton, c.1792" .... (wonder if this could be the "3 Carles ...." number???)

Ewan MacColl's 1964 recording of "The Braes o' Balquither" found here :   https://www.youtube.com/watch?v=3tyYZLeVrLs
is slower and different to the Alma Gluck, Jock Tamson's Bairns et al version, but I can't lay my hands on the liner notes of his LP at present to add detail.

Geordie McIntyre and Alison McMorland though, are noted as singing their variant from the Greig-Duncan folk song collection.

R-J