Hi Dave,
Don't forget you are dealing with a song at least as old as 1620 and 'little' could have several contemporary meanings, not necessarily small in stature. I would suggest perhaps 'young' or even 'lower status' than the Barnards. There may be other possibilities. It could also even be just a term of endearment.

Conversely, it could be a nickname or irony as in 'Little John' of Sherwood fame and of the same period.