Gravitational force is between two object caused by energy in mass. Here when you are in a mine the radius of the earth in case of calculating gravity is reduced to the length between you and the center.
This means the mass of earth is decreasing even though the distance is decreasing. Relative to the decrease in distance squared the decrease in the mass of the second object(earth) is more. As a result your weight decreases.
Explanation: that means as you descend into the earth, all of the mass in all the shells above you gets canceled. If the centre of the earth were not molten iron, but instead hollowed out, you would be weightless inside.
The physics problem is actually a little more general. It applies to inverse square force laws such as the electrical force. So if you put an electron inside a positively or negatively charged sphere, it will also have a net force on it of zero.
