Seems very wasteful to be taking extra, unnecessary flights for perks, no matter how big. I don’t care about the fliers’ money, that’s theirs to do what they want with. But the environmental costs are non-nil (even accounting for the fact that those flights would be going regardless of if they fly on them) and can’t be worth the perks for these privileged few.
It does work harder by weight carried. There is some induced drag for every pound of lift and, in unaccelerated flight (most of it), lift and weight are exactly balanced.
My piston-engine airplane goes about 3% faster on the same fuel flow (power) at the end of a long flight than the start. That’s the effect of reduced drag from the lower weight.
Flying in a plane is basically the most carbon intensive thing normal people do. It's something like 1/4 ton of CO2 per hour per person. Per capita carbon emission in the US are ~15ton/yr.