Standing in a motinless elevator is like standing on the ground.  Your weight (a force) can be represented by a vector pointing down...F=mg

But if the cable holding up the elevator were to snap, your weight vector would disappear because BOTH you and the elevator would be freely falling downward.  Imaging trying to stand on a scale when you are floating around in the box.... (pretty hard to do!)  F=zero

QUESTION:What lies between these two situations?
ANSWER:  If the object accelerates downward, but not freely falling.

It should make sense that your weight would decrease; the snapped cable example has weight becoming zero...
Mathematically speaking, the force becomes F=m(g-a) where g is 9.8m/s/s and a is the downward acceleration.
What if the elevator accelerates upward?

Then you'd feel "mushed" to the floor, in other words it would be like super gravity... F=m(g+a)

What happens when you reach a constant speed either up or down?  Since you are no longer accelerating, you just use F=mg