Southwest is the airline for you. It's my understanding that they play musical chairs. Any fat people who can't get a spot with an empty seat next to them are summarily executed on the tarmac and their blood is used to lubricate the engines.

Truly, there are a million aggravations with public transit. Stinky people, noisy people, nosy people, loud people, etc. Fat people are going to exist. You don't deserve compensation. Get over yourself. As a fat guy, I can say that I am just as uncomfortable as you when flying. To minimize that, I make every effort to not bother others - I pick undesirable seats, I upgrade when I can, and I've even bought an extra seat when the situation required. Most of the fat people I know do the same.