Check in and Weigh in
I thinks the solution relies upon weighing the passenger and their luggage at the point of checking in. Anyone whose combined weight is more than 120kgs has to purchase an additional seat.
This would work perfectly. Those in the body weight range 90kgs - 120kgs would have to either pack very economically or pay up. Those weighing over 120kgs (the clinically obese - 19 stone) would have to buy 2 seats to fly.
Adjust the limits to suit the airline - tight cramped low cost airlines could set the total weight at 110kgs. Easyjet and Ryan Air could set it at 100kgs.
It requires lowering the baggage belt at check in to ground level so that the pax can stand on it with their baggage. No embarrassment, no offence casued.