Like Southwest charging for check in bags, the airline that manages to market this to lighter pax as a way of saving them money is going to be just the first domino to fall. The fruit is there to be picked in terms of less conservative fuel and freight loading.
I'm no airline exec, but the way I'd do it is introduce it slowly using an optional trial period over a year where customers get a discount on their fare when they book if they provide their weight in advance. The discount gets credited at check-in as long as their weight is within tolerance of what they put in the reservation. Offering the carrot like this to start with will get all the punters on board with the idea.
After that, you quietly tweak the online reservation system so that the price on the screen becomes the defacto "heaviest passenger" price and if you enter your actual weight and it is closer to the norm, you get a decent discount to reflect the true cost of carriage. As long as the majority of people feel like they are getting a good deal (which they will, unless they are obese) then they will happily continue to provide the info.
Meanwhile route planners will now have an accurate idea ahead of time now, exactly what the weight of the pax will be. Weigh the hold baggage and assume a nominal 7kg for hand baggage. You could easily have a couple tonnes difference per leg over what you used to assume. That equals big fuel savings over the whole network, and presents an opportunity to optimise the way freight is carried, and even to allocate seating according to optimal CG. If you employed really clever analysts you might be able to save fuel and carry more freight.
Jet A1 is not getting any cheaper. I expect to see this become commonplace before I'm too old to travel anymore.