This is really amazingly retrograde thinking. Modern electronics with accurate load cells could easily establish the REAL take-off weight. Any deviation from the load sheet could then be quickly investigated. Correcting for lift in wind isn't an insuperable problem.
Well, the aviation industry have tried and not found it worthwhile, according to earlier posts.
With a background of designing 24/7/365 reliable embedded systems, using the latest then-available electronics, I've noticed many similar, at first sight surprisingly "retrograde" places in aviation. However, looking deeper into the reliability and other design issues, it has become clearer why the aviation industry in general tends to be cautious introducing new solutions. Sadly, I've also followed several recent aviation projects aspiring to introduce radical new technology, which have failed with many million dollars of losses.
So I'm not dismissing the load cell idea as such, but just want to point out that the road to a solution which is sufficiently economical and robust to displace current practice, may not be near as easy as it looks initially.
The wind issue as an example: Probably not insuperable, but I doubt much research has been done to fully understand all conceivable situations and error sources - as there have been no commercial demand for it so far. So someone would have to pay for that research too.