Not to feed the troll or anything, but yes, the masses and positions of the three weights are evidence about Charon's movement. Why? Because if you calculated Charon's orbit without knowing their masses, positions etc, you'd be less accurate than if you did.

Calculating Charon's orbit without knowing what direction Charon moves in, or even whether it moves at all, is an impossible task. You are substituting "Charon's orbit" for "Charon's movement" in your argument, then acting as though you have made a statement about Charon's movement.

If you all do not grasp why precision in the use of words is absolutely necessary to eliminate bias in natural language, I will drop the point; nevertheless, it remains.