Sadly, the source is yet unknown. It's a tune credited to Christopher Marlowe and is next on my 'Folk Songs' list.
COME, LIVE WITH ME, AND BE MY LOVEFrom the book compiled by Andrew Gant.
Text and melody: W. Chappell, Popular Music of the Olden Time (1859). This song was very popular at the turn of the 17th century. It is quoted by both Shakespeare and Marlowe, and several contemporary sources claim Marlowe as the author. The tune was discovered by Sir John Hawkins 'in a manuscript as old as Shakespeare's time' and it appears in Corkine's Second Book of Ayres (1612).