The issue here is that Samoa Air's fleet of 3 planes are tiny. The smallest has a maximum take off weight of around 1600 kg. 1600 kg of fuel won't even get an A380 from the gate to the runway most of the time. With such planes, calculating the gross weight accurately is vital, unless one wants to have an impromptu swim mid flight.
The other issue, assuming that anti discrimination laws (from many countries) allowed it, would be how the airlines themselves verify it. For Samoa Air, with planes with a max capacity of 13 passengers, it's not that hard. But a full A380 or even a 320 would quickly turn into a farce, most likely. The other issue is that airlines, particularly the LCC operators that would be the most likely to use such a system, have been aggressively cutting costs by reducing staff and pushing people (often quite forcefully) into automated and online check in systems. Are they really going to suddenly turn all that on its head to employ staff to weigh every single passenger and their luggage? No chance that that would ending up costing more than they get back from higher fares, is there?
Most of the comments on such articles on the Fairfax websites just seem to be an excuse to beat up on fat people. Quite a few are even rather explicit about it, taking a sadistic glee in that fat/heavier people will be punished by paying more, as though society doesn't give them a hard enough time as it is.