The ballad from which it gets it's tune is "The Liggar Lady" (#8970 in Steve Roud's folk song index) reprinted in vol. 3 of the Henly and Henderson edition of Burns' poems. Unfortunately I have only vols. 2 and 4. This song seems to be an early 18th century one.

The 'Gallant Grahams' ballad is ZN405 in the broadside ballad index on my website. For the tune see "Cady Laddy" and "Mount your/my/the Baggage" (also "The Captain's Lady") in the CNTYDAN2 and Scots tune indexes there. Here's one copy that's listed there:

X:1
T:Mount your Baggage (Cady Laddie/ I will away..not tarry)
Q:1/4=120
L:1/4
M:C|
K:D
F|\
DFA2| DA B/A/G/F/| GE2F|\
DFA2| Fdc>B| AFF::d/e/|\
f/d/e/c/d2| DA B/A/G/F/|GE2d/e/|\
f/d/e/c/d2| Fd"tr"c>B| AF2d/e/|\
f/d/e/c/d2| DA B/A/G/F/| GE2F|\
DFA2| Fd e/d/c/B/| AF2:|]