Do you weigh less in an elevator going down?
Also, why does weight decrease in elevator?
In a moving lift, the weight of an object changes because the value of g changes to, say, g'' because of the acceleration of the elevator. Here the aceleration of the elevator becomes equal to the object placed in it.
Similarly, what will the scale read when the elevator is accelerating downward? The inertia of the person would prefer to keep moving downward at the constant speed, so the elevator floor and scale must push up on the person to accelerate him upward, slowing him down. Therefore the Normal Force is larger, so the reading on the scale is a number that is GREATER than the true weight.
Consequently, does your weight change in a lift?
The simplest answer to the question of whether your weight changes when you ride in a lift is 'no'. Your weight, being the force with which the Earth pulls down upon you due to gravity, does not vary with speed or acceleration. It does, however, feel like your weight changes when you ride in a lift.
What is your weight in free fall?
A freely falling object has weight W=mg, where W-weight, m-mass of the object and g-acceleration produced due to the earth's gravity. This happens because the normal reaction force exerted on the object in the lift is equal to zero, and normal force equals to mg, which in turn equals the weight of the object.