The tune s referred to by Allan Ramsay in his additional verses (published in 1716) to the 16th century poem 'Christ Kirk on the Green:

"He fits the Floor syne wi' the Bride To Cuttymun and Treeladle, Thick, thick that day."

The first part of the tile refers to 'cuttie(-y)-mun, (a) “a spoon with a small mouth and a short shaft” (Dictionary of the Scots Language). The second part refers to a wooden ladle ( sometmes 'treen' - made of wood'); "tree-ladle, a wooden ladle, gen. in phr. cutty-mun and tree-ladle, the name of an old dance tune" (Dictionary of the Scots Language)

The December 2014 issue of Common stock had an article on the tune and its relatives; you can read it HERE