From a pal in the Great Wen:

John,
I’m sure your mailbox has been inflated with fulsome missives on the weighty topic of porcine poets, beefy balladists and corpulent chroniclers. My mind, never far from my next drink, immediately ran to the imbibing Celts, who had a tendency to run to pudge, though not quite fat — Dylan Thomas, Brendan Behan and even poor sweet Oscar. I also recall that Byron had a tendency towards tubbiness, which he fought vainly, though not in vain, with regular purges and diets of biscuits and vegetable stock. Based on the frequency with which he discoursed on his diet in a collection of his letters I read years ago, he was rather obsessed with his weight.
I would also plump for Ben Jonson, Jonathan Swift (always depicted with a double chin), Hilaire Belloc (hardly the equal of the other half of the portmanteau duo Chesterbelloc, but of increasing girth with age), Les Murray, the later Pablo Neruda and the later John Betjeman (there is clearly a theme here, linking increasing age with avoirdupois).
I recalled that your and my favorite author of inaugural doggerel, Maya Angelou, was a woman of weight, but a quick google search shows her to be well within the bounds of health — perhaps I am thinking of the more prosaic Toni Morrison?
Finally, you may not be aware (though you surely should have suspected) there is a contemporary school of “fat poetry,” which urges us all to “enjoy, enlarge, enlighten and enliven” ourselves. These adiposeurs, to coin a phrase, even have a website.
Warmest regards,
Howard

Thank, buddy. My only quibble would be that while Behan (who described himself as “a drinker with a writing problem”) certainly carried a fair embonpoint, he was a playwright and autobiographist, not a poet. At any rate, I defy you to find anyone who ever read any of his poetry (which I think was all in Irish).

Another reader offers Edward Lear as an instance of a fat poet. Apparently Lear once described himself (in verse) as “perfectly spherical”