The reason for keeping the heavy bits near the centre of gravity is to minimise the moments of inertia about the airplane axes. The easiest way to visualize moment of inertia is to consider the tight rope walker at a circus. He carries a long pole to help him balance. Without the pole it would be much harder to balance because once he started to topple he would fall over too fast to be able to correct his fall. With the pole, he topples slowly with lots of time to correct the fall.

The long pole increases the tight rope walker's moment of inertia. To get a high MOI you need to concentrate weight a long distance from the axis of rotation (the rope in the case of the walker). The bigger the distance, the smaller the weight required for the same MOI.

Of course, if we want an airplane which is responsive to the controls and have a snappy response about all three axes of rotation then we need to keep it's MOI low, and this means concentrating it's weight close to the centre of gravity.

In nature there is no such thing as a free lunch. We have to make many design compromises. Servos close to the control surfaces provide us with short, stiff control rods which minimize free play and dynamic nasties such as flutter, but they also contribute to increasing MOI and consequently degrade the airplane's snappy response. Increased MOI also makes the airplane less sensitive to external disturbances, such as gusts, but requires more powerfull controls when a gross correction is needed.

Note that stability is not involved here. An airplane with a very low MOI can have a fast response, even too fast for a human to control, but still be stable. On the other hand, a big ponderous airplane with a high MOI can be unstable and still able to be flown successfully by a human, although often with some difficulty.

Hope this helps.