I wish the airlines did ask for people's weight. Recently I've flown some flights where the CG and zero fuel weight listed on the weight and balance sheet had to be way off.
They should have a floor scale at the gate. When you check your ticket to the gate agent, you walk across it and it records your weight, including your bags.
When I flew the Beech 1900, I asked people's weight religiously and if I thought they weren't telling the truth, I made them step on a bathroom scale. I don't want to further a stereotype, but the ladies ALWAYS grossly understated their weight.
-Fatty