Moving the CG forward will indeed make the plane more nose heavy. Moving the CG back will make the plane more tail heavy. When you move the CG, you are not simply picking a new spot on the airplane and calling it the "CG". You have to add or shift weight to effectively move the CG. If you select a location forward of the existing CG and place the airplane on a balancer at that new location, what happens? The tail of the plane will fall and you will need to add weight to the front to get it re-balanced thereby making the plane more nose heavy.