From Dick's The Songs of Robert Burns, p. 363:

No. 35. O, wilt thou go wi' me, sweet Tibbie Dunbar. Scots Musical Museum, 1790, No. 207, entitled 'Tibbie Dunbar. Tune, Johnny McGill.' The MS. is in the British Museum. In Law's Museum MS List, Burns has written 'Mr. Burns's old words.' Nothing is known of the subject of the verses, which were written to illustrate the melody. Riddell's Note (not Burns's) in the Interleaved Museum is 'This tune is said to be the composition of John McGill, fiddler, in Girvan.' An old song in the Merry Muses is marked for the tune, the first stanza of which is:--

'Duncan Macleerie and Janet his wife,
They gaed to Kilmarnock to buy a new knife;
But instead of a knife they coft but a bleerie:
"We're very weel sair'd," quo' Duncan Macleerie.'

The nationality of the tune is disputed; on some slender evidence it is claimed as Irish. In Scotland it is now best known with MacNeil's song, Come under my plaidie. The music is in Campbell's Reels, 1778, 31, and Aird's Airs, 1782, ii. No. 119.