As long as the motion of the elevator is uniform, the weight is the same as in a stationary elevator. Additional forces only apply during acceleration/deceleration, not during uniform motion.

F=ma

In  uniform motion the resultant force is null, however in the begin the elevator movement, a not null resultante force is necessary for rmove the elevator from the inertia. The same idea can be applied when the elevator begins to stop. In the two cases you can use the Newton second law