Acceleration, not Force, is constant at a given distance

It is common knowledge that the acceleration due to gravitation of the earth, denoted by 'g' is constant for a given distance from the center of the earth. This is not an approximation, as in this case, the terms actually cancel out.

However, this is often taken to mean, also by the use of Newton's law of reciprocal reaction that (I forgot what I was thinking :p)