We will have the following:
*If a person has a weigth of 500N on Earth, and moves from the ground level to a position high up on a mountain this will affect the gravitational force between the person and the Earth in a very minuscule way. The net change is given only in the gravitational potential energy stored in the person due to the position higher up- And the force between the person and the Earth will be slighly smaller, since the distance is a little bit greater between the center of the Earth and the person.
*We have that they are both acceleration towards each other, the person is falling towards the Earth and the Earth is falling towards the person, but the acceleration of the person towards the Earth is orders of magnitude greater than the Earth falling to the person.