Here's my transcription of the 1-page sheet music image at Levy. (See nutty's link above.) I have modernized the punctuation. Also, since the sheet music shows that line 7 of the first verse is repeated, I have assumed the corresponding lines in verses 2 and 3 also repeat.

BEN BACKSTAY
A Favorite NEW SONG Composed by Mr. DIBDIN
Philadelphia sold by H. & P. Rice No. 50 Market St. between Front & Second Streets

1. Ben Backstay loved the gentle Anna.
Constant as purity was she.
Her honey words, like succ'ring manna,
Cheered him each voyage he made to sea.
One fatal morning saw them parting
While each the other's sorrow dried.
They by the tear that then was starting,
They by the tear that then was starting,
Vowed they'd be constant till they died.

2. At distance from his Anna's beauty,
While roaring winds the sea deform,
Ben sings and well performs his duty,
And braves for love the frightful storm.
Alas, in vain! the vessel battered
On a rock, splitting, opened wide;
While, lacerated, torn, and shattered,
While, lacerated, torn, and shattered,
Ben thought of Anna, sighed, and died.

3. The semblance of each lovely feature
That Ben had worn around his neck,
Where art stood substitute for nature,
A tar, his friend, saved from the wreck,
In fervent hope, while Anna, burning,
Blushed, as she wished to be a bride.
The portrait came. Joy turned to mourning.
The portrait came. Joy turned to mourning.
She saw, grew pale, sunk down, and died.