The usual statement of elevator's problem is: "If the elevator is in a free fall, what is the person's weight?". The answer is obviously zero. In my opinion, a person in falling elevator doesn't give a s*** about his weight.
Your question is more complicated, since you're assuming terminal velocity is reached (either due to friction with air or any other reason). Reaching terminal velocity by the elevator means zero acceleration.
Now, the person in the elevator is not affected by the external forces which oppose gravity force experienced by the elevator. It means that from the perspective of the person, the usual gravitational acceleration trying to push him into the floor of the elevator. However, we know that this headline is completely bizzare: "A man made a hole in elevator's floor and fell to death!". Well, for some elevators this may not be bizzare at all.
So, why the person won't fall? Due to the same force which prevents this when the elevator is at rest - the Normal force. The floor of elevator pushes the person up and this force equalizes gravitational force.
In fact, the fact that elevator moves at constant velocity is irrelevant. The weight of the person will be the same as if the elevator had been at rest.
There is very famous though experiment named "Galileo's ship" which is described in Dialogues - it's whole point is to argue that there is no experiment one can make inside a ship, which will tell whether the ship moves with constant speed or at rest. Being "at rest" is just a special case of constant motion (speed = 0).