Now here's my theory:

The truth is, that Mary Ellen Carter was a lady who plied her trade in the bars in some seaport town, probably Canadian. She was past the best earning years for her business, and very fond of beer, which had caused her to put on quite a bit of weight, but she continued to try to make her living as best she could.

Anyway, one dark rainy night in October, she took on quite a bit of beer in the company of six or eight members of the crew of a small vessel that was in port there, and ended up agreeing to provide for the immediate needs of all of them, for a "bulk rate," as it were. Unfortunately, as they were proceeding back to her rooms, all of them sort of hanging on to one another to keep upright, she slipped on the wet cobblestones and fell heavily. She was uninjured, being well padded, but she was so well padded, and so out of balance from the beer, that it amounted to a distinct challenge for all the crew members with her, even all working together, to get her back on her feet so she could take them home and complete their business.

At this point, the action of the song begins.

Now: Go out and sing the song to an audience, and keep a straight face!

Peter.