Shouldn't the hobbits all be fat fucks?

In the book, they are all kinda fat. Hobbits are said to generally be pretty stout. That said, the Shire is an agrarian society and doing farm work every day would burn off a good chunk of that weight. Plus you're walking everywhere.

Funnily enough, contrary to Sean Astin's portrayal, Sam would probably be the most physically fit hobbit in the Fellowship. Merry, Pippin, and Frodo are essentially rich nobles who sit on their ass all day whereas Sam actually works. Frodo, in fact, is outright fat in the book. He describes himself as looking "rather flabby" and there are a few mentions of him losing weight on the trek to Mordor.