Is the force of gravity greater on more massive objects?

Yes.

According to Newton's Second Law, force is the product of mass and acceleration. F=m*a

The acceleration for every massive object is the same near the earth's surface, regardless of its mass. This is why two objects will hit the ground at the same time, even if they have different mass, as long as air resistance isn't a problem.

One way to think about it is this: heavier objects have more inertia, so gravity has to use more force to get it to move at the same acceleration as a lighter object.