Why doesn't an object falling from an airplane continue to accelerate?

The object's weight varies as it nears the ground.
Air resistance on the object will eventually equal the force of gravity.
Gravity's force diminishes as the object nears the ground.
Hitting the ground stops the object's acceleration.

Air resistance on the object will eventually equal the force of gravity. This phenomenon is known as terminal velocity, where the object reaches a maximum speed at which the force of air resistance balances out the force of gravity. Once this point is reached, the object's acceleration stops and it continues to fall at a constant speed.