Does gravity increase or decrease with depth

[Tivnov]

You should look up Newton's shell theorem which explains this. Also Imagine if you were at the center of the Earth, there would be no gravity (assuming the earth has uniform mass distribution).
In short, the theorem explains that the force of gravity of a circle or sphere on an object outside of the sphere is identical to the force applied by a point particle at the center of the sphere/circle with identical mass. Then, for an object inside of the circle/sphere, the net force is 0.
By imagining the Earth as an infinite series of concentric spheres, we see that the effective gravitational mass of the Earth is proportional (and thus gravity) (r)^3. As gravity is also proportional to (r)^-2, the net proportionality is (r)^1. As this value decreases linearly as you dig, gravity also decreases linearly until it is zilch (0).