Typically a rocket that is stabilised for X size motor will not neccesarily be stable for a larger motor.
Basic principal is that a rocket must have the center of gravity (balance point) forward of the center of pressure (this is where the forces exerted by air passing by are centered)
lets say your rocket is balanced 1 body diameter ahead of your CP with the smaller motor. Put a string at the balance point. Now put the bigger heavier motor in. You will find that the center of gravity has moved back closer to the aft end. Since the CP does not change you are no longer balanced 1 body diameter ahead of your CP. Nose weight is now needed.
Some people keep extra nosecones balanced for specific motors.
Myself I usually balance my rockets to the weight of the largest motor I anticipate ever using in it.
I am kicking around an idea for some of my larger cluster rockets (where engine weight can differ quite a bit) where I would have a threaded rod in the nose where I can put removable weights.
Hope this helps