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Agreed, however they would still have a reasonably good idea of the weighjt and if it was well under AUW then it is not a major issue. (though it really should be known)Apart from the safety point of view of pax and/or crew on board, if the crew can't work out how many people and how much baggage is loaded, I can't see how the pilots can work out their take-off weight.
They would know how much fuel they had and having a reasonable guestimate of weight could fairly accurately work out fuel burn. (half a dozen or so pax would have little or no impact on fuel burn)As far as I know, the aircraft could've been over-loaded (as per the manfacturer's specs), or it could've ran out of fuel before arriving its intended destination.