I’ve always assumed you pay extra because multiple people have to carry the bag around after you check it, and that’s harder/more dangerous at higher weights.
In warehouses, you gotta go get your lift belt and often a partner if something is over a certain weight, and you aren’t covered by workman’s comp if you just try to do it quickly without those, so it’s a serious hassle.
I always assumed it was more about the conveyors and such your bag goes through before even getting to those folks. Heavier bags mean more wear and tear and maintenance on those machines.
Honestly, it’s probably a little bit of both along with just deterring some cohort of people from bringing too much stuff because they don’t want to pay the fees.
The extra fuel cost doesn’t even remotely compare to the cost of an injured baggage handler and their lost wages.
Using that logic, the extra charge doesn’t come close to the cost of an injured baggage handler and their lost wages. If that was the reason, they would reject it outright or split it into multiple bags.