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You weigh less only while the elevator's upward speed is decreasing, or downward speed is increasing.

In each case, the acceleration of the elevator is in a direction opposite to the acceleration of gravity.

The result of that is that the total acceleration acting on you is less than usual, and your weight is less.

Note that in a sealed container, such as a space ship or an elevator, there's no way for you to tell

the difference between acceleration and a gravitational field.

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