I think the flight attendant has to escort him to the gate...
It costs them more fuel to haul an obese person, period. It's physics. One could argue that if you need more than one seat you're requiring the same fuel as two smaller people occupying both seats, but then they sell tickets based on seats, not people (important distinction).
They have published dimensions for carry-on luggage now - if the bag is too big, it gets checked. Now we can't just go tossing fat people into the belly of the aircraft with Grandma's pant suits, but I think clearly defined "people size" should be published. If you are wider than 'X' in a seated position, you need to pay up for the extra space you will use.
One could also argue that heavy people might be seated to the rear to save fuel (aft CG improves aircraft performance), but that's so politically incorrect that it'd never fly, pun intended.
I already pay more based on how much I annualy drive. It's called fuel tax. The more I drive, the more fuel I use, ergo the more fuel tax I pay. I believe if you check your fuel receipts, you will find yourself in a similar pay-to-play situation.