The Roud Folk Song Index lists it at number 601 (Laws N6), grouped with The Rich Merchant's Daughter / The Press Gang / The Lady and the Sailor and so on. Two examples from Gardener & Chickering are listed: their version A (text only, beginning "Some say I'll go crazy, some say I'll run mad") came from Chauncey Leach, Kalkaska, Michigan, 1934, and their version B (tune and text, "I am a young girl, and my fortune is sad") was from Charles Bunting, Alger, Michigan, 1935.

In this particular case, most of the narrative has disappeared and been replaced with floating verses. There are various broadside editions at  Bodleian Library Broadside Ballads:

The lady and sailor

Mostly the man is a sailor already, but in one edition, a little earlier than the others, he is a weaver by trade pressed to sea at the merchant's behest:

The lady and weaver

The story then proceeds as usual.