airlines could do it as a promo.
Imagine the free press they would receive. Just like O'Leary from Ryanair, when he wants millions in free publicity, he just says
"we're going to charge 2 euros to use the loo onboard" & all the media gets up in arms & then 2 weeks later, he says they've decided against it.
But it's not that difficult really.
They could have fares eg. like
1) up to 80kgs inc everything, person, all bags
2) up to 100kgs
3) up to 120kgs
etc.
They already weigh checked bags. Only difference is passenger would have to jump on same scales as well.