Newton's 3rd Law tells us that if two objects interact via some force, then the value one exerts on the other have the same magnitude but opposite directions. Newton's 2nd Law tells us that the value of this force is F=ma. So, for two objects with different masses, if the forces they are exerting on each other are equal (as they must be by Newton's 3rd Law), the accelerations they are experimenting must necessarily be different.
