Nicholas,
Two methods of calculating the weight and balance are used. One involves standard weights for male and female adults and children, and for baggage. The other method involves using actual weights.
Due to the immense difficulties of weighing each passenger and each bag and calculating precisely where each item goes, standard weights are preferred. When standard weights are used, bags are considered either "standard" or "heavy." A bag which weights in excess of what a standard bag should weigh is considered "heavy," and a higher weight penalty is applied to the airplane. Even if the bag is a pound over the standard weight, it becomes a "heavy bag," and may count for as much as two standard bags.
From a revenue perspective, the aircraft can only hold so much weight. Even though a bag may not weigh twice as much, once it becomes a "heavy bag," the airline must consider the bag as having weighed the full standard "heavy" amount.
Getting standard weights for bags in a lower cargo space makes sorting the bags easier. Can you imagine weighing each individual bag, then sorting them one by one to establish balance? The bags are packed in tightly, in no particular order, when weighed and determined to be "standard." This saves time and still allows the flight to be made safely.
Weight and balance are critical considerations for aircraft control, and for performance. Weight affects speeds, but balance is also very important. We consider the weight of the fuel, and even the way in which that weight continues to be distributed as it burns off in flight. Likewise, we carefully consider the placement of passengers and cargo as we determine the best way to safely load the airplane.