This airline error shows just how important weight is in a flight. Everyone should be weighed not just bags. Instead of putting your bags on the weigher you should stand on it and weigh yourself and bags.
Current system, properly functioning, properly monitored works perfectly well on large, heavy even when empty aircraft because of the chosen value of the standard weights, plus the way stats usually work out with large population number. What you do still need to look out for is you not carrying a lot of outliers such as a squad of several dozen NFL players...
It doesn't work out so well with smaller numbers because of the chance of one or two people being overweight/underweight skewing the figures away from anything derived by statistical values. Also for small aircraft the chances are the mass of the passengers/crew and their bags might make up a much bigger percentage of the total aircraft weight - That's the reason for weighing people before flights on really small aircraft..
I'm really not sure how popular weighing everybody would be in these days of on-line check-in and bag drops...