The True Nature of Gravity

Uhm. No.

F=ma

Your mass doesn't change when moving from Earth to space. Thus, experiencing weightlessness in space is evidence of the decreased acceleration due to gravity.

The weightlessness felt in space is because of the orbit around the earth. When in orbit, one is always accelerating towards the earth at a rate equal to about g, but a little less because of the increased distance.

This seems kind of needless. By the time that you get to falling distances high enough that you would actually see a difference in acceleration, an object would have reached terminal velocity.

Also, it is true that all objects have the same acceleration, regardless of mass. A more massive object is being pulled to the earth with more force, but since it has more mass it also takes more to move it. The equation F=ma proves it.