Why can deck-edge elevators weigh more?

What creates the weight difference between centerline and deck-edge aircraft elevators?

Mostly the structure needed to support and stabilize an elevator at the ship's edge, not the elevator platform itself.

A centerline elevator is supported within the ship's structure, while a deck-edge platform moves a heavy aircraft load outside the hull. The elevator surface itself need not be dramatically heavier. The additional demand comes from guiding, supporting, and stabilizing an off-center moving mass in a rolling ship. That engineering penalty has to be weighed against the hangar space and unobstructed flight deck gained by moving the opening to the edge.