A couple from Allan Sherman:

To the tune of Molly Malone:
She wheels her wheelbarrow
Through streets that are narrow,
Her barrow is narrow, her hips are too wide.
So wherever she wheels it,
The neighborhood feels it,
Her girdle keeps scraping the homes on each side.

In Dublin's fair city,
Where girls are so pretty,
My Molly stands out 'cause she weighs 18 stone.
(That's 256 pounds.)
I don't mind her fat--but,
It's not only that--but,
She's cockeyed and muscle-bound, Molly Malone.

[Fact check: 18 stone is actually 252 pounds]

To the tune of Polly Wolly Doodle:
Oh I diet all day and I diet all night,
It's enough to drive me bats.
Got no gravy or potatoes,
'Cause the whole refrigerator's
Fulla polyunsaturated fats.

Fare thee well, Metrecal,
And the others of that ilk.
Let the diet start tomorrow,
'Cause today I'll drown my sorrow
In a double malted milk.