Answer:
It flies when it's on and floats coming off.
Only one color, but not one size. Stuck at the bottom, yet easily flies. Present in sun, but not in rain. Doing no harm, and feeling no pain.
What is that which, though black itself, enlightens the world without burning?
You seek it out, when your hunger is ripe. It sits on four legs, and smokes a pipe.
A precious stone, as clear as diamond. Seek it out while the sun's near the horizon. Though you can walk on water with its power, try to keep it, and it'll vanish in an hour.
Special abilities and brightly colored underwear are all you need to be one of these.