If we bring a mass from far away toward the Earth, the gravitational force increases...the closer it gets, the bigger the force. This is certainly true when the mass is outside the Earth - what happens if we bring it right to the surface and then keep going, tunneling into the Earth?
If you're inside the Earth, as you get closer to the center of the Earth does the force of gravity increase, decrease, or stay the same?
A parallel question is this one - what is the force of gravity on an object at the center of the Earth?
The net force is zero - there's as much mass pulling you one direction as there is pulling the opposite way. The force of gravity decreases as you move from the surface to the center.
This is a consequence of Gauss' Law for Gravity. One implication of this is that inside a spherical shell of mass, the force of gravity due to the shell is zero. Outside the shell, the force is exactly the same as that from a point mass of the same mass as the shell, placed at the center of the shell.