For large passenger jets operating for big airlines, there is a 'Dispatcher' or 'Turn-round Manager' (TRM) whose function is to co-ordinate all the ground processes prior to departure.
The TRM will have access to the aircraft's basic weight and CG schedule and will input the expected passenger load, baggage, freight and fuel figures. This will produce a 'provisional load-sheet' showing the forecast Zero Fuel Weight (ZFW) Taxi Weight, Take-Off Weight (TOW) and Landing Weight. It will also show the ZFW CG and the TOW CG. These last two are normally expressed as as a percentage of Mean Aerodynamic Chord (MAC) rather than a distance from a fixed datum.
The flight crew use the provisional figures and the ATIS data to load the FMC and to calculate take-off thrust and speeds. The FMC may provide some of these figures but it is a case of GIGO as others have mentioned. Eventually all passengers and freight are loaded and the TRM is in a position to finalise the figures. These may vary from those forecast due to missing/extra passengers, changes in the number of freight pallets loaded, etc. At some point before take-off, the final figures are passed to the flight crew in the form of a 'final load-sheet'. This may occur prior to doors closed or else during the taxi-out.
The flight crew review the final figures and check whether or not they differ from the provisional figures by more than a pre-determined percentage or figure. If the final figures are within the tolerance, there is no need to adjust anything and the take-off is accomplished as planned. If however the final figures differ by more than the allowed tolerance, the FMC must be partially reloaded and the take-off performance recalculated.
The FMC may run its own 'reasonable' check of the entered figures and may show a warning message if it detects a gross error. Some aircraft are fitted with pressure or extension sensors on the gear which may be used to accomplish this cross-check.