As air does have weight and so density, if clouds are made up of particles, then they must have weight and density too.
The estimated cumulus cloud density is about 0.5 gram per cubic meter. The weight of a cloud can be measured as the weight of the water droplets in the cloud. As 1 cubic kilometer (km3) cloud contains 1 billion cubic meters and a droplet is 0.5 grams, there are 1,000,000,000 x 0.5 = 500,000,000 grams of water droplets in a cloud. That is about 500,000 kilograms or 1.1 million pounds (about 551 tons).
However, “heavy” clouds still float on air because the air below it is even heavier; the density of the same volume of cloud material is less than the density of the same amount of dry air, i.e the moist air in clouds is less dense than dry air.