There is a "force", can't think of it's name, that applies to a "motionless" mass that resists motion. Otherwise it take no force to move a still mass.
In the example I gave, the earth did not gain or loose it's mass = gravity proportions, i.e. it didn't get bigger or smaller (in a mass sense). It is my understanding that the earth's gravity has a certain value regardless of whether these two objects are in its gravitational field.
And yet the 2 different balls experienced the same rate of change in distance under the power of the same value of force.
Perhaps a better example is to imagine a large box in space far away from any noticeable gravity caused by masses, imagine yourself in the box. The inside of the box is a coordinate system, and you are at rest relative to that coordinate system.
A rope is attached to the box and the box is pulled thru space at an accelerating speed. You will feel a force towards the opposite side of the box as the rope. You will move in that same direction. As you move, take a pen, a 12 oz lead ball, and a grain of sand out of your shirt pocket and notice which one hits the side of the box first.
They, and you, all arrive together, as a result of a single value force in the opposite direction. That is what I meant by "steady"