Here's why:

* Acceleration due to gravity: The acceleration of an object falling freely near the Earth's surface is due to gravity. This acceleration is constant for all objects, regardless of their mass or starting height.

* Neglecting air resistance: We usually assume that air resistance is negligible in these types of problems. If we consider air resistance, the heavier ball might have slightly less acceleration due to the air pushing back on it.

In summary: The only factor that affects the acceleration of a falling object is gravity (and air resistance, which we're ignoring).