This is really more an issue on plane than movie theaters since it is easy to go see a movie when it is not packed. When one buys a plane ticket, they are effectively renting the space of a single seat. If you cannot fit into it, then you should have bought 2. People next to you should not have to share the space they paid for.
Yes, overweight customers should pay extra for seats in planes or in movie theaters, because they are using the space that someone else would want to use. The vast majority of the time, weight is something that can be controlled. If a person needs to use two seats, they are taking a seat away from someone else.
Really, it does not sound fair, but if I am sitting next to an overweight person on a plane who is taking up part of my seat that is not fair to me. Sure, the seats should be bigger, but they are not going to be and so we need to make some people buy two seats.
Just because someone is overweight does not mean they should have to pay more. That would be insulting to them and then they will get depressed and feel bad about themselves. That should not be our goal. If someone is that overweight just give them the extra seat for free.
It's not as if overweight people are unaware of it prior to being taxed for a seat, it's not going to be some revelation that changes their lives. I find it hard to believe that overweight passengers hinder a plane so badly that fees are needed to compensate them, so really it's just to make people feel bad more than anything else. It's a different matter if they literally prevent a second seat from being usable, but if they're charged just by hitting a point on the scale that's wrong.
I do not believe overweight customers should have to pay for extra seats on airplanes or in movie theaters. Airplane seats have become smaller and smaller over the years to help airlines become more profitable. While I believe businesses should make a profit, sometimes I think they take their antics too far. This is a prime example.