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.

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.

Right. But wouldn't that system still count just one adult and assign them, e.g., 69kg of "standard weight"?

>low error tolerance

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.

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.