Like DonR said ^^^: or, if you remove the bowls (painful on the later bikes) you can see the bits in the bowls that are causing the stuck floats.
It is possible that the strainer inside the gas tank is crumbling now, and has open spots that let tiny crud make it into the carbs, not good. You can replace that filter, but you must do it by draining the tank, then removing the old screen and plugging in the new one: it is available from Honda. I have one of those kits around here somewhere.