I think they should have to provide a seat that will fit the obese person.
If you take up extra space, you should pay for it. I also have no interest in sharing my seat, which I paid for, which an obese person. It is a little harsh to find out at the last minute that you aren't going to be able to infringe on other people's seat space, but these obese folks will learn the rules soon enough.
In response to above comments, SUV drivers already pay higher taxes because their vehicles burn more fuel. And two skinny people aren't allowed to occupy the same seat because it's unsafe.