My Dad, who passed away at 88 this January, used to sing that song to me when I was little. I think it’s called “Too Fat Polka”.
I remembered it from I was a kid.
Too Fat Polka
Here’s a silly ditty,
You can sing it right away
Now, here is what you say
So sing it while you may
Here’s a silly jingle,
You can sing it night or noon
Here’s the words, that’s all you need
‘Cause I just sang the tune:
Oh, I don’t want her, you can have her
She’s too fat for me
She’s too fat for me...
https://www.google.com/search?q=Too+Fat+Polka+Andrews+Sisters&oq=too&aqs=chrome.0.69i59l2j69i57j69i61j69i60j69i65j69i60j69i65.3307j0j4&sourceid=chrome&ie=UTF-8