The weight of individual bags and individual passengers becomes more and more important as the airplane becomes smaller, as individual weights have a proportionately greater impact on balance, as well as performance.
When standard weights are used, these values are applied to the final weight numbers for performance calculation (V speeds, climb performance, etc).
When passengers sit in seats, balance is a fairly simple matter with standard weights; the precise location of each estimated (standard) weight is fixed by the seat position.
When bags are packed in a cargo area, the values become a little more critical, as variances, packed closer together, can add up to larger changes from the norm. That is, each bag, ten pounds over or under, for example, makes a significant change from the expected value over the space of a packed cargo compartment, than it does for passengers in their seats. This becomes a balance issue.
Performance numbers are based on the weight of the aircraft and the ambient temperature; performance numbers are calculated just prior to takeoff, and just prior to landing. Performance is also calculated for the flight, by dispatchers or schedulers, when determining how much fuel to carry, etc. A heavy airplanes will require more thrust and more fuel for a given flight than a light one.
The actual takeoff weight of the airplane can vary somewhat from the planned or estimated weight that the schedulers use. The amount of variance that can be tolerated depends on the airplane in question. A big airplane can handle a bigger weight difference.
If our schedulers estimate the fuel for our trip based on a given weight, for example, they have used flight planning data to set up the route, considering forecast winds, to have us arriving at the destination with a particular fuel reserve. When we get the flight plan, generally two hours before our departure, this has all been precalculated. If our weight is not the same as the weight that the flight planners used, then we could have a problem.
We have a 10,000 lb variance. That is, unless the difference between our takeoff weight and the planned takeoff weight exceeds 10,000 lbs, we don't need to recalculate our flight planned performance. If it does exceed that value, we are required to have a new flight release issued, which recalculates our enroute fuel burn and other factors associated with the flight. This is a company policy applicable to our B747 aircraft. Obviously with smaller airplanes, that much difference would be entirely unacceptable.
Our takeoff fuel for a given trip can vary 30,000 to 40,000 lbs depending on weight, for the same length of leg. That is to say, a lighter airplane may require forty thousand pounds less fuel for a given trip than a heavier one. We normally try to land with a minimum of thirty to forty thousand pounds. Mistaking the planned weight could conceivably result in insufficient fuel for a trip. Obviously underestimating weight may also result in serious takeoff penalties; our takeoff roll is long enough that we always see the red lights at the end of the runway during the takeoff. We've got to have realistic numbers when planning the takeoff.
Ironically, even in a big airplane, the positioning of people can have a noticeable impact. When calculating an empty takeoff, which is just crew, the addition of an extra person or two on the upper deck means we need to add ballast fuel to the center fuel tank to make the airplane balance for takeoff. In smaller airplanes, in some cases one can feel the airplane require pitch trim changes, in some cases, when someone walks through the cabin or changes seats. In the extreme case, in a hang glider...one controls the entire aircraft simply by shifting weight.