Question

Why doesn’t a heavy object accelerate more than a light object when they are free falling

Answer 1

I like to think of it this way:

... Gravity pulls on heavy objects with more force than light objects.
(That's why they're "heavy".)

... Heavy objects are the ones with more mass.  Light objects are the ones with less mass.

... Gravity is pulling on more mass with more force, and on less mass with less force.

... But from Newton's 2nd law of motion, we know that it takes more force to accelerate more mass, and less force to accelerate less mass. 
That's exactly what gravity is doing.  So the heavy object with more mass, and the light object with less mass, wind up with the same acceleration.

There you go.  With zero math !