The problem is, how are they going to make the distinction between really obese people and people that are tall and pack some weight due to being this tall. Let's say they ask your weight alone, that wouldn't be enough in a scenario like this, so weight and height. Who's going to provide the statistics that tells them what is obese when getting these numbers? What if people refuse to give it to them? Are they going to refuse them the flight? Too many questions, too much red tape I'm thinking.
Sell it as a discount for passengers who are willing to stand, _luggage_in_hand_, on the scales to be weighed.
If airlines choose to charge additional for passengers occupying a single seat based upon weight than they should have to publish the weight a standard ticket is based upon and also have to issue immediate partial refunds, not as vouchers, to passengers under that weight. I would love to save some money on my 60lb 9 year old who takes less fuel to transport.
I would go the other direction: let's pack thin people two by seats We all pay the same, but with the higher density of well packed thin people, the airlines would double their profit.