Southwest will win unless they get an overweight judge who wants to get back for years of not being treated as an equal in society...
However, I have watched many episodes of Airline and do feel that the person of size policy needs to be changed and better enforced.
If I were a person of size, I would expect that once at each airport, an airline ticketing or gate employee would stop and question me. Southwest could lose a lawsuit if one of these people required to buy a ticket could prove they flew <x> southwest flights in the prior few days/weeks without buying a 2nd ticket. If a judge saw lax enforcement of a rule, then yes it could be a question of harrassment or racial profiling.
Granted, the airport is not a private place, so people currently DO hear the questions being asked, so they need to continue to make sure that the questions are as unoffensive as possible. Have a support group for persons struggling with obesity write the questions, that way the airline is not making up the verbage. Just like a hotel has to be discreet about giving you a room # without reading it to you, perhaps Southwest should start giving a card to the passenger instead of asking them the question out loud. The person can respond by pointing to the option (not fly, buy a 2nd seat, get measured, etc). SITTING on the plane to see if you take up another seat is a waste of employee and other passengers time, and THAT is more humiliating in my eyes. "Mommy what is that fat person doing walking on the airplane before we board... Mommy why are they back at the ticket counter red in the face". Southwest should have a policy that if you are more than <x> inches around, you buy another seat or get a refund. Fixed weight limit isn't as good of a policy (body builders etc). There is a fixed limit on luggage weight, fixed weight limit on helicopters, and Fixed limit at amusement parks (42" tall to ride this ride). Southwest could give the passenger a garment measuring tape and watch them measure themselves. To further not humiliate them they could give them the option of walking to a more private area with an employee to do so, but I think just by making it a classy looking fabric tape (solid black, etc.. not a yellow measuring tape, and there is no reason to have it list every inch... just a "red" mark that says too big would do fine. Have it in the rules when they book their ticket or get their online reservation confirmation, so that it's not a surprise to anyone.
Also, since this is a big hassle and a part of the job that airline employees don't like to do, and passengers don't like to partake in, they should get some sort of a verification if they don't want to do another field obesity test for the next <x> days. That way should another employee stop and show them the same rule list, they could whip out their card, the employee could thank them and tell them to enjoy their flight, with VERY LITTLE confrontation. I think the worse thing they are doing is loosely or irregularly enforcing the rules and letting the people make a fool of themselves trying to squeeze into the seat to prove themselves to the employees. Everyone that does that on the airline show is like "AHA see I told you so" or "darn I have to buy another seat".