How does the gravitational anomaly measured at the Earth's surface and produced by a subsurface body depend on its depth and on the density contrast of the body relative to its surroundings?
The gravitational anomaly (delta_g) changes linearly with the density contrast, and proportionally to the inverse square of depth. That's simply a version of the 'Universal Law of Gravitation'. Here is an example for the anomaly created by an spherical anomalous spherical body with a density difference of delta_rho relative to the surrounding density. G is the known Gravitational Constant: