Are clouds heavier than air?

Clouds are gatherings of water droplets floating in the air. Water droplets above a given size fall down as rain. But what about the water droplets forming the cloud—aren’t they also heavier than air?

My own guess is that clouds are held aloft on uprising air currents. I know this is true of some clouds. My question is whether this is always true. Can you have a cloud that stays aloft in completely still air?

I suppose that a way for a cloud to stay aloft in completely still air is if each droplet is falling down, but the ones at the bottom of the cloud evaporate, while further ones are condensing at the top. In that case it is continually ‘raining’ inside the cloud, but the whole looks still from a distance. So then a follow-up question: is this case common?