In my opinion, I think Southwest Airlines doesn't discriminate anything to the overweight passengers. First, they play fair. if there's no charge for the overweight passengers, and they still placing them to sit in the regular seats, others passengers will be very distracted. They have to buy 2 tickets or else they won't take the flight or not accepted to in the airlines. And every plane company always counting their load in their planes. That's why if the passengers bringing an overweight luggage, they will be charge more. So, it's just as the same as the passenger. You overweight, and you will be charge more.
Second, if they don't want to buy 2 tickets, take a diet. Lose weight is the best thing to prevent cholesterol and others sickness(obesity, etc). Other than in planes, overweight person is distracting others in other place or situation. For example, in the bus, train, etc. Even when they fart, it will smells bad because inside their stomach will be very dirty of any kind of food combine together like garbage. They are very lazy on doing something, dirty because they lazy to throw away their rubbish to the 5 feet trash near them. Looks like I'm very sensitive to the overweight person. Sorry if it's out of topic.
Third, back to the airline issue, if the overweight passenger haven't bought the other ticket at the day before the flight, and the tickets is all sold out, they will strictly cannot go into the plane. And the money will return back to them. That's my opinion about that. There will be a rules & regulations in every airlines which the passengers have to follow.
That's all, my opinion in this article is to be strict to an overweight person to think about others nor to distract them. If you overweight, you will be charged more fares in any other occasions and situations not just in airlines. There's no easy answer to this. Just my opinion. Thanks!