A heavy object falls with the acceleration as a light object during free fall. why?

A heavy object falls with the acceleration as a light object during free fall because:

Heavy things have a large gravitational force and also have less acceleration. So both the effects exactly cancel and make the falling objects to have the same acceleration irrespective of mass.

Free fall is a unique motion which has only gravitational force that acts on an object. Objects that undergo free fall experience only have the influence of gravity and not any other force.

So when we apply newton's second law of gravity which is:

where,

F is the force

m is the mass

a is the acceleration

For example: When a 1000 kg elephant and a 1 kg rat fall from the same height,

The acceleration can be calculated as follows:

For elephant: F = 10000 N and m = 1000 kg. So,

For rat :  F = 10 N and m = 1 kg

Thus,

Hence, it shows that both the animals have the same acceleration irrespective of their mass.