Same goes for passengers.
I'm all for letting the market handle it.
1. One big difference is that freight transportation involves handling of the product in a way that passenger transportation does not. Freight is inanimate and has to be handled often at multiple different points in the transportation process. Almost all passengers, on the other hand, move themselves to and from their seats.
2. Related to #1 ... To get a sense of how big a factor the "handling" process is in transportation, just look at container shipping. Because a shipping container filled with styrofoam peanuts is handled the same way as a container filled with a densely packaged product, there is no difference in shipping costs between the two.
Personally, I have no problem with an airline charging based on passenger weight. But you can be sure that there would be hell to pay when half of the overweight passengers come up with some kind of "disability" that makes the whole plan unworkable.