Clouds are collections of water droplets or, at higher altitudes, water ice crystals. So, honestly, why would they stay up there? It is not like snow flakes, for example, hang around or anything.
The title question is legitimate. We cannot invoke old Archimedes and claim that the clouds float like a hydrogen balloon would. Hydrogen is lighter than air. Water is not.
Yes, but clouds are not balloons anyway, you may answer to that. The stuff they are made of is minuscule, and maybe those minuscule things can float. The dead-pan reply to that is: Yes, they can. We see that.
And the size of the droplets is important, just in a different way than you may think. As with everything it is a combination of many processes.
A cloud droplet of a few microns in size falls, but only slowly. It experiences resistance as it moves. It reaches its so-called terminal velocity almost at once. In addition, air flowing through the cloud pushes the droplet upwards as well. You may think of it in this way: Normally, an object, let us say a house, would stand against the wind. As the object becomes lighter and smaller this is no longer true. The wind may push it around like a snow flake and it does.
It is all about the balance and where nature finds it. It always is.