The big problem here is that it would be abused by the airlines as an excuse to charge more and add more seats. The seats are already too small and with far too little leg room. At least they are from my experience in most European airlines (and not just the budget ones).
I am not over wieght and often struggle to get comfortable. The funniest thing is the advice they give you for exercising whilst in your seat on longer flights - if you can do those whilst staying in your seat and not pulling a muscle or poking your neighbours in the eye - you are a midget contortionist.
I have also been on flights where there were some seats that it was physically impossible for anyone of a modest height to actually sit in them. My father in law is only as little taller than me and slim - he simply could not get his legs into the seat even twisted at a painfull angle. Luckily the flight was not fully booked and he was able to get a seat elsewhere.
Also, how would a "fatty" paying extra actually help you? Do you honestly think that the airline isn't going to fill the seat next to them even if they have paid extra?
The human race is getting larger and the seating on flights needs to reflect this - before we even think about "unnaturally large" people.
I would say that the seats should be roomy enough to accomodate a decent percentile of the human population. If that means less seats, fewer passengers and higher prices then so be it. Being able to fly somewhere (cheaply) is not a right. It is a symptom of the current "must have" society that everything has to be cheap and available to everyone or its considered some sort of infringement of your rights.
When I grew up I was taught that if you can't afford something then you didn't get it. It didn't mean you were any less of a person, it was just out of your reach. If you wanted it badly enough you saved up until you could afford it. I still live by that principle.