This is either the most idiotic discussion I've seen on APC ( and that's saying something), or you're all in on a lame April Fools joke. Besides the inherent unfairness of such a policy (one small example: women will pay less to fly than men on average), the logistics of such a system are absurd. Forget online check-in; go to the airport several hours in advance, get on a scale, then pay your fare.
People are not the same as cargo. Their weight has virtually nothing to do with how much it costs to move them in an airplane.
Let's all just forget the whole supply and demand system that actually determines airfares. Why would we want to use that when we can just hope that a lot of fat people fly?
Who comes up with this stuff?