It's even dumber-sounding than that (though there are safety margins built into the system).
If you have a flight which is performance-limited, they will limit baggage hold (checked) bags which are weighed and force you to carry that same bag into the cabin (where it is not weighed and added to the performance calculations).
I seem to recall that there are specific weights used for aircraft where the passengers are overwhelmingly different from typical adults (think of an NFL football team flying to/from a game), but that general variances among passengers do not need adjustments to performance.
If my airline operates a charter flight with non-standard passengers (like your NFL example), the FAA requires that we ask passengers for their weight prior to boarding or actually weigh them at the door. If I recall correctly, we must do this for all chartered flights and not only sports teams, but I’d have to look it up to be certain.
To my knowledge no airline accounts for general variances among passengers leaving Mississippi as opposed to, say, Colorado. The standard passenger weights do change in the winter vs the summer to account for heavier clothing.
It's not just weight, but also distribution. I've been on small regional aircraft (think 16 to 32 seats) where the flight crew has asked passengers to change seats in order to get a better balance of weight across the aircraft.
I took a helicopter flight once where your seat was determined solely by your weight and that of the other passengers. I felt bad for the person that paid the same as me and got the middle rear, while I got to hang out the front door.
From what I understand passenger planes and cargo planes alike need to balance and distribute the mass onboard. If they don't they could run into aerodynamic issues. It's a enter of mass vs center of lift kind of thing. However the balance would have to be really far off for anything serious to happen.
It could, but practically speaking the difference between a full-size adult and a very heavy adult tends to be constrained by the physical limits of the seating capacity, requiring passengers that could be overweight enough to impact the flight safety constraints to buy two seats.
It has enormous margin during all-engine takeoff performance, so it's not at all surprising that the takeoff continued successfully.
The performance calcs are done to ensure safety in a one-engine inoperative case.
The performance calculations for all multi-engine turbojets require at least a balanced field (simplified meaning: that you can experience an engine failure at the most adverse moment in the takeoff sequence and either bring the aircraft to a halt on the runway surface [including EMAS or other stopway surface] or you can continue the takeoff and meet initial obstacle clearance and second stage climb requirements with the most adverse engine inoperative and maximum thrust from the working engine).
That's why this is a serious deviation, even though turbofan engines rarely fail. 737s do reduced power takeoffs as a matter of economic optimization. The error here caused too little power to be commanded during the takeoff.
In a sense, it's not too terribly low; the end result here was that the plane took off outside of the correct flight envelope but well within a safe and controllable envelope (given a loading difference that - back of the napkin calculation - is 2% of its dry weight).
But AAIB pursues this sort of thing aggressively, under the principle of "Don't assume everything is safe because the O-rings didn't fail if the O-rings are showing not-understood ablation."
The plane took off without a problem, so this was within the error tolerance. You could imagine cases (e.g. charter flights full of women) where it could be an issue, though.
If the cargo and the passengers aren't distributed and weight accounted for properly the typical calculations you make to take off based on weight stop working... potentially entirely / catastrophically. It has happened before resulting in crashes.
A few overweight passengers can't do that, but a combo of too many passengers and etc can have an impact.
This is a real concern for some operators. It’s a particular issue in Samoa, where there is a really bad obesity problem.
(One of the local airlines used to charge for excess passenger weight as well as luggage)
TLDR: 5481 crashed because the figure used as the average weight of a person for the purposes of calculating the planes centre of gravity was from before America got fat.
