Hello! I know this thread is old, but I found a version of this song in the book "A Sailor's Song-bag: An American rebel in an English prison, 1777-1779" by George Gibson Carey. The book encompasses songs collected by one Timothy Conner, a privateer, during his time at Forton Prison in Falmouth. Here's the version included:

Come come pretty Sally and set you down by me
And tell me the age you are upon
Tis sixteen and one six month past and gone
And I'm weary of lying alone, I'm weary of lying alone

When I was eleven sweet heart I had seven
But now I've got never a one
And I vow and declare I'll die and despair
If I lie any longer alone, if I lie any longer alone

A sister of mine was married at nine
And Children had many a one
And I vow and declare I'll die in despair
If I lie any longer alone, if I lie any longer alone

I wish some young man would take me by the hand
And make me a Wife of his own
For I vow and declare I'll die in despair
If I lie any longer alone, if I lie any longer alone

Down in yonder Bower there grows a fine Flower
I'll pluck it and call it my own
But Flowers will fade and so will a Maid
And I'm weary of lying alone, and I'm weary of lying alone

The seas are deep I cannot wade them
Neither have I wings for to fly
I wish that I had some little small boat
For to ferry my love and I, for to ferry my love and I

...

There isn't much additional information (Conner does not include who specifically he collected songs from), and the last added line is as far as I know unique to this source.

Here's a link to the whole book at archive.org :

Sailor's Song-Bag on the Internet Archive

- Mary