In the CBS news story United To Charge Heavier Passengers Twice To Fly we hear about how passengers that don't fit into one seat now need to buy a ticket for a second seat next to them. This is reasonable because they are taking up 2 seats. If a parent is traveling with a child in their lap they still need to pay an extra fare even though that child isn't taking up a seat.
However, what the airlines are missing at the moment is the weight discount approach. In order to reduce how much they offend their passengers they should charge a higher price and offer discounts for each pound your total weight is under their threshold. $1/pound sounds reasonable to me. Someone who's luggage and body weighs in at 240 lbs should be given a $60 refund to their credit card once they've checked-in at the airport assuming that a 300 lbs threshold per person is set. Of course there would also have to be a minimum because you're taking up a seat.
What effect would this have? Easy, people who are lighter and/or travel with lighter luggage will suddenly start traveling with that airline. The airline is carrying less weight and using less fuel and can offer a more competitive price to its customers. The other airlines have to handle the heavy weights.