What a fascinating question, isn't it? I guess the practical answer for a passenger is to get to the aircraft before any fatties, whether or not seats are allocated, so that you'll be the one already sitting down and keeping the armrest down which, as has been hinted, probably gives an moral advantage if the fattie tries to take the next-door seat and can't get in.
If he/she then squashes you with a mass of lard you can complain loudly.
The difficulty for the crew is illustrated neatly by Bealzebub, a Captain, a master of the committee decision, saying:
if called upon to make a decision, I would base that decision on their (ie CC) recommendation.
while lowcostdolly, who is evidently what it says on the tin, tells us;
As a last resort I would consult the Captain if I could not resolve the problem myself
I do realise that these two statements, seen in their contexts, are not totally contradictory, but neither poster really answered the question of what decision they would come to when decision time is upon them. And that's understandable; there's no real rule, and there needs to be as the obese take over the earth.