I'm pretty big (I have been very fat in the past, now it's closer to just being "hefty" and it being evident I lift weights), and I just avoid flying economy. Even when I got myself to the point of a waist to height ratio that was on the lower end of what seems to get listed as the healthy range, I was still taller and broader-shouldered than most people.
I don't think airlines help matters trying to fit in as many seats as they can, but there's no real way round it as long as people are chasing cheap flights - I'm happy to pay more for increased comfort, but I can't imagine trying to fill a plane with people like me is a workable business model.
30% larger seats for people who take up 30% more space - and which cost 30% more - sounds just fine to me, but I think it only actually solves the problem if airlines can make people who need them use them, and at that point you're going to get a lot of vocal complaining about it.
Weight as such is a bit of a red herring for seat fitment. If you weigh someone with a decent amount of muscle, you'd be surprised how heavy they are relative to their size. If you're looking at take off weight and plane loading etc that's fair enough, but in terms of fitting in a seat, well, it's about whether you fit in a seat!
I don't like these kinds of programmes as I think they're crass and voyeuristic, but while I can see an argument for the programme being "fat shaming", airline seating and the reality of life in general isn't.
Having been obese, the undercurrent of general opinion that fat people have themselves to blame is bang on the money in most cases. Those with explicit medical reasons behind it are the outliers, most just take on food at higher quantity and lower quality than corresponds to their level of physical activity.
I don't think the approaches to weight loss that are normally promoted are particularly helpful either, but that's a whole different discussion.