ORIGINAL: Time Pilot
Secondly, how will moving the weight away from the CG effect the way an airplane flies? So rather than the heavier stuff located almost under the CG, it will be moved fore and aft. I’m thinking the plane may be slower to react and to stop when it is moving about the point of balance, but also may make it more stable at the same time.
As Paul describes, moving weight outward will increase the moment of inertia of the airplane, which means the movements of the aircraft will occur more sluggishly. However, your overall stability will not change, so long as you are not moving the CG (or the AC).
I like to do this to make the plane "look" more stable in the air- note that not only will the plane react more sluggishly to control inputs but also external influences, such as bumps in the air. This is good for scale looking flight, not good for aerobatics. You can, by the way, also add weight to each wingtip (if you can tolerate the overall weight increase) to increase the lateral moment of inertia if the plane gets bumped around the roll axis too much for your desired flying appearance.
Also, if you have a plane that is marginally stable, increasing the moment of inertia will exacerbate the stability issue (although the stability itself does not change), as you have to fight the controls a bit more as the plane's reaction lags the input a bit.