Next time you fly, try to be the last person to board. As you walk through first class see if there are any empty seats. If so, and you are seated next to a fat person, just walk to the front and in a calm but firm voice, explain the situation to the flight attendant. Tell him/her that you do not want to make a scene but you just can't fit in the seat.
It is an unwritten policy of most airlines that they would rather give you a first class seat rather than have a confrontation.
Works every time.
Thanks for the advice - I hope I won't have to try it, but if I do I'll at least have an idea of what to say.