I agree: if for no other reason, because the heavier object ATTRACTS the other body more, which will have a small but real velocity component up towards the falling object!
Your opinion was once universally held; but experimentation has shown that heavy and light objects fall at the same speed. Each falling object is not only attracted to the earth in proportion to its mass, but it [the falling object] also has inertia that resists the motion, so the falling object's mass cancels itself out. All that's left is the earth and the gravitational constant, which are the same for all falling objects.
Yes, but you forgot it has proportionately more mass to accelerate, so it falls at the same rate.