I have been having a lot of swelling in my legs after my longer flights. I found these socks that I was told would keep the swelling down, reduce fatigue and have a positive effect on circulation and DVT. After 10 days and a few long flights, they really helped. They are thinner than cotton athletic socks, about the same thickness as dress socks.
DeCompressor socks
These are worth trying.
I don't often wear socks, but when I do ...