What are the factors that affect the force of gravity between two objects?

Interesting question. Consider the formula that governs the gravitational formula

F = G * m1 * m2 / r^2

G is the gravitational constant. It does not change no matter where you are in the inverse, nor is it found to be different under normal circumstances. Since you have asked this in biology, you can assume that the circumstances are always normal./

m1 and m2 are masses in kg. The mass is invariant as well anywhere in the universe, except perhaps near or in a black hole.

r^2 is a distance in meters.

So the Force of gravity (in Newtons) varies directly as the masses involved and inversely as the distance squared.