An increase of height increases the time that the object will fall, and therefore the final velocity of the falling object.
Watch the example shown on the following video:
It increases the amount of potential energy with respect to the gravitational center.
A "falling" object implies a gravitational field. In fact, all orbital motions are related to this concept of the height of a falling mass.
A 'dropped' object converts its potential energy derived from it height into kinetic energy as it accelerates. "Terminal Velocity" only applies in the presence of a resistive force, such as wind resistance. Otherwise, Newton's Laws say that a mass will continue to accelerate as long as a force is applied to it. Of course, Einstein showed that the speed of light in a vacuum IS a limit!