Aero Academic
The process of confirming an aircraft's total weight and its center of gravity fall within limits published by the manufacturer before flight.
Weight and balance is the process of confirming, before every flight, that an aircraft's total weight does not exceed its maximum certificated weight and that its center of gravity (CG) falls within the forward and aft limits published in the Pilot's Operating Handbook. Both conditions must be satisfied — an aircraft can be within its weight limit and still be unsafe to fly if the CG is out of range.
An aircraft loaded with the CG too far aft becomes less stable and can be difficult or impossible to recover from a stall, since the tail's ability to force the nose down is reduced. A CG too far forward increases stall speed and can make the aircraft difficult to flare for landing, since there may be insufficient elevator authority to raise the nose.
Manufacturers often express arms and moments as a moment index (the moment divided by a constant such as 100 or 1,000) purely to keep the numbers manageable when heavy items sit on long arms, which is a frequent source of confusion for candidates encountering weight-and-balance problems for the first time.