what's scary is the amount of guesswork that goes into loading a plane. The trouble with averages is that most loads aren't average. So you build in a healthy safety margin. Ok, that saves lives, costs money and is susceptible to outliners. (Like, possibly, this case.)
How hard/expensive would it be to have three large pads on the runway apron. As the plan rolls over the pads the weight carried by each set of wheels is relayed to the pilot and recorded. A quick calculation based on plane type would allow an accurate determination of the cg. An informed go/no go decision can then be made. The information can also be used to improve loading of future cargos.
I've driven through highway weigh scales where the truck only has to slow down below a certain speed and the weight shows up on a big sign. I'm imagining something similar here. Thoughts?