We must first make the distinction between weight and "apparent
weight". The definition of "weight" is just the magnitude of the force
of gravity on an object, which wont change much unless you take the
elevator very far from the surface of the earth. What I think you are
talking about is how heavy something feels, or "apparent weight", so
this is what I will discuss below.
Isaac Newton told us something that will help here. Objects in
motion tend to stay in motion unless acted on by something else. That
may sound complicated, but an elevator is a great way to see this.
When the elevator is moving, we will weigh our normal weight. Since
we are already moving at the same speed as the elevator (up or down),
nothing is affecting us to change our weight. However, when the
elevator starts to go or stops, our body resists it. Let's say we are
going down. The elevator stops. According to Newton, our body wants to
keep going, but the floor will not let us keep moving. So for a short
time, we are pushed into the floor more and our weight goes up.
The same thing works when the elevator starts moving. Our body is
happy to be standing still. But if the elevator starts to go down, our
body wants to stay still. That's why you feel light at first when the
elevator starts to go down. Once the elevator starts to move, we get
used to moving and we don't feel it anymore.
(republished on 07/12/06)