Answer
Your weight would decrease.
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 of the same density, so you are lighter. Your weight will decrease the closer you are to the Earth’s center.
This is discussed on pages 171-172, and shown in Figure 9.23.
