Two questions decide whether an aeroplane is safe to load: how much is on board, and where it sits. Get the total mass wrong and you degrade every aspect of performance and eat into the structural margin the designer built in. Get the centre of gravity (CG) wrong and you change how the aeroplane handles, in the worst case to the point where you cannot control or recover it. Both are the pilot's legal responsibility, and both are checked first when an accident is investigated. The good news is that the sums are simple arithmetic, done on the ground, before anything goes wrong.
(In aviation we say "mass" rather than "weight", but for loading purposes treat them as the same thing.)
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