If clouds are not falling, it is not because they are lighter than air, but because they are caught in a dynamic atmospheric system that keeps them aloft.
Clouds are made up of air, water vapor, water droplets and ice crystals. These last two components are denser than air. So even though clouds appear to be light as feathers, they usually weigh hundreds of thousands of tons. They should therefore naturally fall.
Clouds and the atmosphere, a dynamic system
This would be without taking into account the fact that clouds and the atmosphere are not static physical systems. At the heart of the cloud, the droplets are in motion. It even happens that some come out of the cloud. However, the surrounding atmosphere being very dry, they evaporate quickly and the limits of the cloud remain well marked.
When droplets seek to escape from the bottom of the cloud, at speeds that remain extremely low, the updrafts of the atmosphere are usually sufficient to compensate for their fall.
When the clouds fall from the sky
However, the updrafts sometimes are not strong enough, and the temperature and pressure conditions allow the droplets to aggregate and gain speed. They then form raindrops and then we can say that the clouds are falling on our heads!