I've been quite shocked by the opinions on here.
I've worked for several different airlines as a flight dispatcher which means, among other things, I've been responsible for determining the fuel required for a flight, and have 1 main issue with charging passengers based on their weight:-
The operating cost for the flight is much the same regardless of whether the aircraft is full or empty. Let's take the example of a Boeing 757 which, depending on the configuration, can carry 235 passengers, and let's say it's operating a flight from Birmingham to Malaga, which is approximately a 2.5 hour flight. The difference in fuel load between an empty and a full flight is around 1 tonne, which sounds a lot, but is based on an empty flight fuel requirement of around 12 tonnes. This is an 8% difference, which is certainly not negligible.
However, this is not the end of the story. Airlines use a formula known as 'Cost Index', which helps them make the flight as economical as possible. There are literally dozens of parameters built into this formula, but the payload weight is one of them. Assuming all other factors are equal, if the payload weight was higher (and therefore more fuel required), then the cruising speed of the flight will be reduced, which will reduce fuel consumption (at the expense of increasing flight time), and therefore mitigating the increased fuel for payload.
This formula is run for each and every flight, and a different cost index is produced prior to takeoff (I personally don't know the specific formula, as it's run by computers, but I do know that it includes parameters such as payload weight, flight time, trip distance, weather, air traffic control delays, flight crew salary, insurance and so on).
Also, airlines use average passenger weights when determining the payload. The average weights used varies between airlines, but at one of the airlines I worked at, a male weight was 85kg, female was 75kg, and a child 50kg. This takes into account the fact that some passengers will be heavier than these figures, and some will be lighter.
As far as the comparison between excess passenger weight and excess baggage weight, I agree that the laws of physics don't differentiate between the 2. However, airlines are under increasing competition and pressure to reduce airfares, yet their costs are almost identical regardless of how heavy or light a load they operate a flight with, and they do have to make money. It's just that charging for excess baggage is deemed socially acceptable, and charging for excess passenger weight (currently) isn't.