jjw004 asks:
"I suppose that a ball traveling the fastest will cause the most damage to a person "due to the extra weight"

Response:
And I suppose that the concept of mass increasing with velocity is new to you thus you are unaware of the fact that the effect is relativistic and was covered in essentially perfect detail by Einstein.

Paul:

Of course gravity becomes weaker as one approaches the center of the earth. If the earth were hollow and an object were to be placed into the center of the hollow earth it would feel on gravity except related to gravitational anomalies (such as Mt. Everest), the moon, the sun, etc.

Why? Because the mass of the earth would be equally spread around them pulling equally in all directions.

DA Morgan