This song is beginning to look like it's borrowed some from a lost theater song of the second half of the 1670s. ZN3203 in my broadside ballad index is, "The Willow-Green, Or Distressed Lovers Complaint", 'To a new Tune, called, the willow green, Sung by Musicians, and in the Theater.' The tune direction here is good evidence that the broadside ballad is an expansion of a theater song. One verse of the broadside goes:

My love sleeps on another man's pillow,
  were it but for an hour or two,
Then i'de leave off this mournfull willow
  then Love see what you can do:
Was ever man more kind in tryal,
  to a Lass then I have been,
But she to me doth prove disloyal,
  and makes me wear the willow green.

No wedding of the disloyal lover in this, or her death, but the verse above is quite similar to lines in copies of "The Nobleman's Wedding". Steve Roud's folk song index notes a broadside copy of "The Nobleman's Wedding" in the Madden collection (Cambridge), but I haven't been able to find a copy on the Bodley Ballads website.

The green willow also occurs in "All Round My Hat" and "All Round My Hat" in JFSS #34, 1930, starts with the first verse of "All Round My Hat" then turns into "The Nobleman's Wedding", and concludes with the "All Round My Hat" verse. It is noted there that some versions of "The Nobleman's Wedding" (including that one) were sung to the tune "All Round My Hat".

ZN2784 in my broadside ballad index was sung to the tune of "My Love sleeps on another mans Pillow. Or, The Willow Green", but only "The willow green" is cited for ZN3587.

^^