Okay, I did my own math. Looking quickly with google it seems a plan like a 747 might weigh around 800,00 lbs and might carry up to 400-500 people depending on the type. So lets say we've got 450 people, each 150 lbs and carrying 50 lbs of luggage (which is a lot of luggage, more than I think people normally bring) so 450 person/luggage units each 200 lbs is 90,000, which is a little over 10% of the weight of the plane. To me that says that the difference between one person being 120 lbs and one being 190 lbs isn't that much. If the plane were transporting a team of sumo wrestlers I could see a need to charge by weight, but since there are already weight limits on luggage and people don't vary so dramatically in weight it doesn't make much sense to me to price things based on weight.
AND how would you even buy a ticket when your weight could change by the day of your flight? I can just imagine making everyone wait (ha!) to pay on the day of the flight, standing in even longer lines to get properly weighed in front of everyone. I mean, the time wasted doing that probably would negate any extra money the airlines would make, and it would piss off a lot of people.