The singer sings the praises of handsome Molly, noting that "Sailing round the ocean, sailing round the sea, I'll think of handsome Molly wherever she may be." She proves less than faithful, but he loves her still
It is my firm belief that this is a version of the "Farewell Ballymoney/Loving Hannah" family of songs (with which it shares several verses and the whole plot, as well as melodic similarities). In this I actually agree with Roud.
Paul Stamler, however, observes that "The plotline is similar, but I'd be inclined to split off 'Molly' and class the 'went to church on Sunday' verse as a floater. Look at it this way -- if you ask old-time musicians to play 'Handsome Molly' about 95% can do so, but if you ask them to play 'Farewell Ballymoney' at least 95% will go, 'Hah?'"
I still think I'm right, but it is certainly true that "Molly" has achieved independent circulation (though all the versions I hear seem to come ultimately from the Grayson & Whitter recording), and so we list it as a separate song. - RBW
The SharpAp version shows that the song, with lyrics very close to those sung by Whitter, was circulating some nine years before he made his very-influential recording. Whitter, it should be noted, came from the same area in Virginia where the SharpAp version was collected. - PJS