Carrying extra weight on an airplane to save a few gallons of fuel at the destination?  That's ironic.
"Ironic"? I think it is clever. Some carry 50 kilos of clothing; I make do with about four pounds. First things first.

Lots of people take their bikes by air. HOWEVER, that is expensive and inconvenient, because you have to partially disassemble the bike (usually) and fit it into a special and expensive carton, which is then probably thrown away and burned at point of destination. BTW, when I travel I do not take my laptop or other nonessentials. I usually take with me a few liters of good tap water (in carry-on luggage) and also a few pounds of food. This is a good allocation for when one is stranded in an airport overnight.

Once again, I question: Why go anywhere without a bike?

When it burns more petroleum than leaving it behind.
An additional fifty pounds might burn an additional quart or two of kerosene on a transatlantic run. You have any idea of how heavy those babies are? And anyway, I just lost twenty pounds and plan to lose another fifteen. Better to take a bike along than extra blubber.

I've always thought that obese people should pay more on planes.

That begs the question of how much you could save by renting something at the destination.