Ultimately while the principle is good - and, as an overweight person, I'd have no problem paying more if it was done fairly - no airline would ever introduce this fairly. Once they've raised the price for fatter people, why, as a business, would they lower the price for thinner people to balance it out? Why not just take more profit? Think back to when smoking was banned on most airlines, the airlines didn't think "…
I don't know the truth of it, but I see no reason to not simply add onto the bag allowance and put in a scale as described.