So apparently in 1968 Sports Illustrated actually commissioned William Pene du Bois to write and illustrate a children's story called Beat The Queen, which was later published as a standalone book as Porko von Popbutton.
Porko's the nickname of a very, uh, round kid who becomes a star hockey goalie at his fat camp/boarding school. I think the moral of the story is, fat kid learns to love being fat, which, for 1968, seems very ahead of its time.
But I confess, I wouldn't know, because I couldn't finish the story, which runs for 29 freaking screens on SI's archive. Americans may have embraced their fat in the last forty years, but our children's books have gotten lean.
Buy Porko van Popbutton, a real book, on Amazon [amazon via great but forgotten]
How bizarre - I remember having this read out loud by the teacher in class. Probably 4th grade or something.
I loved this book and was thrilled to find a copy at the library used book sale a few years ago. I will only say that the ending is not as you describe and leave it at that.