There are many interrelated songs, going back to "The Lass of Roch Royal," Child # 76, but the particular song as sung by Kathleen Battle stems from a ballad like "The False True-Lover," published in 1906 by H. M. Belden and collected in Missouri. It has most of the elements she includes in the song. Variants are known from elsewhere. Some verses are floaters, i. e., they are borrowed from other songs.
The circumstances and original authors are long forgotten.

I will post lyrics of "The False True-Lover" and a couple of related ballads.