Some aircraft do « weigh » themselves. Freighter 747´s being an example. There are of course tolérances, and in the event of a big enough discrepancy the load sheet is taken as Gospel. So far from infallible. Then again what system is. As to installing it on pax aircraft, well it would be back to risk, added benefit vs the cost of installation and regular calibration. So it ain’t going to fly.
I assume most manufacturer’s build sufficient padding in to flex/ derate calculations to cater for most shortfalls or cock ups.
The average adult (Caucasian) male, or female for that matter, hasn’t weighed in at the notional weights for some years.