CG and Moment of Inertia
CG location along the X-axis (i.e., fore/aft) impacts both static and dynamic longitudinal stability. Statically, the tail lift must be adjusted (stabilizer and/or elevator position) to trim the pitching moments. Dynamically, the further aft the cg goes, the lower the dynamic stability. As CG goes aft, it takes less control surface deflection to pitch the airplane, but the inherent damping of the short period reduces as well.
Moment of inertia impacts the angular acceleration that is generated when a control input is made. The biggest impact on roll moment of inertia is the amount of fuel in the wing tanks. Roll inertia is highest at takeoff and steadily reduces as fuel is burned. Pitch inertia depends on how the payload is distributed along the fuselage. Often the term "dumbbell" is used to describe load distribution with most of the weight either near the nose or the tail.
Handling qualities need to be assessed for conditions representing the range of both cg locations and moments of inertia that will be encountered. When stability augmentation control laws are involved, these variations in airplane configuration must be addressed during control system design.