Well, we can and do cry discrimination on just about anything these days. I don't care if they pay by weight or by seat. My issue is safety: If the person cannot fit into one seat, then it stands to reason if they're crammed into it, they'll have a hard time getting out of it. That's not safe.
I don't care why they're obese - it's completely irrelevant. If you take your infant on an airplane and book a seat for them, you pay. They usually sit on mom or dad's lap. If you are overweight and need two seats to fit comfortably, you should pay. And the safety protocols should be followed, ie., armrests should be down, seatbelts should be buckle-able. If they can't do that, then take the train or bus.
The last plane I was on was very small and I don't think an overweight person could have gotten into the aisle, much less the space (between the seat chair and seat back in front of them) even to get into a seat. I also would not like to pay for being squashed because of someone else's size. Like Linkat said, we paid for the seat we're in, not 3/4 of it.
And overweight people should sit by the window so they don't impede their row-mates in case of an emergency.
Just my 2 cents' worth.
Edit: Oh, and I just watched a show on airline crashes - it seems they used a 175 lb average for each passenger and they've had to revise it to 200 lbs. A considerably overweight person could be as much as double that - might seem insignificant, but if you had a few of these, it would throw all their numbers out, so they should definitely weigh people as they check in. Some airlines are doing this as a case study so we'll see what happens with that.