Extracting 5.4% of the ticket price and making it pay-by-weight (or, rather, by the proportion of the total margin weight you make up) seems fair. On the other hand, 5.4% is a pretty small number compared to the other costs associated with "pay by weight". Lots of people would be, justifiably or not, angry about paying more because they are fatter, taller, or not a child even if that is only a few dollars per hundred on the ticket price.
On the other hand, as a tall person I would strongly support being able to pay marginally more for more legroom. Many airlines do this with a tiered model ('premium economy', 'extra comfort', etc), and it works really well for me.
What's worse is this. Suppose you have 2 groups with each a normal distributed variable (like weight, height, money, likelihood of criminal intent, ...) and let's say a 1% difference in the peak (which is what everyone will always report, standard deviations are also always different, but nobody ever reports them, but when people say Asians are less tall than Caucasians in 1% of cases (real figure is about 6%), this is what they mean). To make things simple, lets say
group A ~ N(100, 10)
group B ~ N(101, 10)
(N(100, 10) is like the "standard" normal distribution for things without reasonable units)
What do you see in practice ? Suppose you meet someone (randomly) from group A and someone (again, uniform random) from group B. What are the chances the member from group A is heavier/taller/richer/more criminal/... than the member of group B ?
E(X > Y, X ~= N(101, 10), Y ~= N(100, 10)) ~ 59%
So in our example, if you meet an Caucasian and an Asian, and there's 1% height difference between the groups, the chance is about 60% that the Caucasian is taller than the Asian. If taken the real figure, 6% difference, then the chance becomes 91%.
This is the problem that causes racism. Tiny differences in a normally distributed variable make a large difference in actual encounters.
Car insurers charge young people more money, despite their youth being outside of their control.
It's dangerously close to an argument such as "People of color have to pay more or can't use this service at all" or "Blonde hair blue eyes" you know?
I don't know how you confused discrimination with murder, but you should probably double check a dictionary.
My point is, don't bring up a flawed argument that's used to support unfair discrimination to attack another argument. That's nothing more than a strawman.
There's also a difference between charging someone for actual expenses, and charging someone for presumed future expenses. And there's a difference between someone being charged for what they use, and someone being paid, or not, for purely indirect costs not related to their performance while on the job.
Now, if a 120 lb woman was charged twice as much as a 120 lb man to fly, your analogy might be more applicable.
While those facts are true, they don't improve the quality of your analogy, the situation you're bringing up does not stack up the same way as (theoretically) charging someone per pound to fly on a plane. There might be reasons that charging by weight is discriminatory, but you're not convincing me.
Charging by X is always discriminatory (on the basis of X), the questions are whether it is morally or legally acceptable discrimination, not whether it is discrimination at all.
People would plan and pack differently if they weren't shielded from the economics of flight this way.
I have been on a few non-commercial flights, and they always make me step on a scale before I get on the plane.
The weight variation makes a big difference for smaller airplanes. Big airplanes can use a statistical average for weight calculations, but small ones cannot.
The weight calculation is necessary to compute fuel load and takeoff distance, for example.
As I recall, there was a major airline crash once because the airplane was overweight compared to its calculated weight. Since then the airlines revised the average passenger weight upwards.