Scales measure weight by measuring the force they need to exert on the object on them,to make the net vertical force on it to become zero.And so They measure the normal force.
Now if we put a scale in an elevator and put something on it,when the elevator is going up,its bottom surface exerts a force on the scale to carry it and the scale exerts a force on the object on it to carry it with itself and that force is in addition to the force to counter the weight of the object and so the normal force is increased and the scale shows a number bigger than the object's weight in an un-accelerated frame.
But when the elevator is going down.Its a bit more strange but I think I can say that in this situation,the elevator's room is directly subject to the force of the elevator's engine and so it accelerates down but the scale and the object just tend to be at rest.So when the elevator accelerates down,the scale and the object stop at rest momentarily till they feel that the normal force provided by the bottom surface of the elevator is removed and so they free fall for a very brief moment.That brief moment of free fall is experienced by the scale and the object as a decrease in weight.And so the scale shows a smaller value for the weight of the object compared to its weight in an un-accelerated frame.