We know that Force applied on an object is equal to the product of its mass and acceleration.

Now, it is given to us that Gravitational force acts on all objects in proportion to their masses, that is, Force is proportional to mass. This is possible only if the acceleration (due to gravity) is constant for a heavy object as well as a lighter object. Since the acceleration is constant, therefore, all the objects (heavy or light) fall at the same speed.