I may have to recant. "Tweedside" is called "Down Tweedside" in the late 17th century Blaikie MS, and this may come from the last line of the first verse of "Wallifou fa' the Cat", "Come down Tweedside to me". So we have two possible tunes with "You London lads be merry/sorry", and there's not much similarity between them. The latter tune should perhaps more properly be called "Wilt thou be willful still, my Jo".