More information: Some of the same words occur in an even older song, The Maidens Lamentation
, printed in the 1670's.

A version in the Bodleian Broadside collection starts

Alas my dearest joy, why wilt thou leave me
Of thy sweet company, do not bereave me
I shall but pine away if thou go from me
Then prethee dearest, stay & do not wrong me

Why wilt thou cross the seas to fight with strangers
When thou mayst live at ease, free from all dangers
I'le fold thee in mine arms, nothing shall grive thee
I'le keep thee from all harms, dear do not leave me

Tune is "I am so deep in love or Cupid's Courtesie" - I haven't yet checked them out