Not displacement (volume), but pressure from velocity: lift. The amount of lift by definition has to equal the weight of the aircraft at 1G.

... and the force of that lift on the plane has an equal and opposite on the air. A Heavier plane disturbs the air more.

Weight of airplane = mass of air displaced per second * velocity of air.

The weight of the airplane is a force downward, the air must match that force, either by throwing a lot of air with little velocity, or a less air, faster.