The dry operational weight, the payload and the fuel on board are the major factors determining the actual weight of an aircraft.
While the aircraft maximum weight is limited by structural capabilities, the location of its centre of gravity (CG) is limited by stability issues. In fact, the location of the CG affects the aircraft stability and, consequently, its controllability. These two values (weight and CG) can also affect the maximum load factors allowed by the manufacturer according to the aircraft category; normal, utility, acrobatic, etc.
The maximum weight of an aircraft and its centre of gravity limits (fwd and aft) can be found in the POH or equivalent. The manufacturer usually specifies the maximum zero fuel weight, the maximum take-off weight, the maximum landing weight, etc.
The aircraft weight and its CG position for the various stages of flight must be known before the flight and the PIC is responsible to ensure that these values are within the prescribed limits. In order to acomplish this, a load sheet - specifying the quantity of fuel and the payload and its location - is calculated.
The standard passenger weights, used in the calculation of the loadsheet, are prescribed by the Regulatory Authority which issues the Air Operator Certificate (AOC). For example, see the EASA Regulation (EU) 965/2012 on air operations - Annex IV – Part-CAT CAT.POL.MAB
The mobile application allows you to practice the calculation of the loadsheet for some common trainer aircrafts. Have fun!