If you work out the number of aircraft verses number of airports would it be easier to install weighbridges at airports? Sure it would be expensive, and airports with multiple runways would need a few however there are advantages. You could have a large illuminated sign telling the pilots the weight and this could be recorded so that the authorities / ATC Tower have records in case of incidents. It would be much easier to control calibration of the airport weighbridges than it would to control the calibration of every aircraft in the world, and an un-calibrated weight and balance computer is more dangerous than no computer at all. Also I doubt built in weight and balance computers would ever be a no go item on the MEL so any unscrupulous operators are likely to ignore failures.
Of course, you can argue that it's a bit late finding out that your overweight when you arrive at the hold, however the costs and inconvenience caused to the operator would soon make people solve the problems that led to the overweight in the first place.
Just a thought.!