Well I can speak for commercial aviation, where takeoff weight does have a few non-arbitrary consequences such as what sort of approaches and turns you can make and how much wake you produce. Also, wingspan has already reached its maximum in terms of what can fit in an airport, so now it's just about how heavy planes can get within that limit. But yes, it's as arbitrary as anything.

The space shuttle would be biggest but I'd argue it took off with a rocket, which isn't lifting off using the air but rather in spite of it. Then on the way down, it could only glide and not support itself straight and level. Again, as arbitrary as you like. It's all a miracle they can fly!