Hell yeah they should, and here's why... I'm a pretty skinny girl, I also used to fly a hell of a lot (Sadly not so much over the last few years - I miss it). As a photographer I was quite often transporting a fair amount of equipment with me, nothing is more annoying that being 4kg over the 20kg allowance, and having to pay extra, when the person in front must be at least twice my weight. In total, me and my baggage weigh less than them, so why am I the one paying more?
I get that sometimes being fat is a medical condition, and I have sympathy for these people, I really do. But most of the time it's down to nothing except laziness, so why should I pay more for a few extra Kg, when they weight far more than me. It's their own fault, and they deserve to pay for it!
Furthermore sitting next to fat people on a plane is disgusting, the constant eating, the spilling food down their front (Why do so many fat people seem to be messy eaters?), the noises they make (What is it with fat people and those weird grunting noises), and while I was born without a sense of smell my partner informs me that they smell gross (I assume it's mostly sweat?). Sitting next to them on an 8 hour flight is horrible, so I get very angry when I've had to pay for than them.
Anyone coming close to spilling over the edge of their seat, should be forced to buy 2, and if they didn't sort that out before the flight, not my problem. Throw them off before take off, if they don't take other people in to account then that's their own problem. In the event that someone does buy 2 seats, I would of course allow them twice the baggage allowance, and twice the personal weight before I began to feel they should be paying more, it's only fair that if they've paid twice, then they can weight twice as much right?
There should be a total baggage and person weight, and anyone who exceeds it, should have to pay... personally I see this being good for fat people, gives them some motivation to sort themselves out. I have no more sympathy for fat people (Assuming it's not down to a medical condition) than I have for crack head, they get themselves in their own mess, they can get themselves out of it, until they do then can pay a little extra.