The Earth has a higher density closer toward the center.
Work Step by Step
Inside of a spherical shell, the gravitational field is zero. You are effectively within a spherical shell whose thickness is the depth of the mine shaft, and standing on the surface of a smaller planet. If the Earth had uniform mass density, your weight would decrease as you went deeper. This is discussed on pages 171-172, and shown in Figure 9.23. The observed increase in weight at the surface of the "smaller planet" shows that the Earth has a higher density closer toward the center. You have more mass closer to the center than expected from a uniform density model. This explains why you are pulled downward with more force than expected.