Yes. Our air is primarily composed of nitrogen and oxygen, but it always has some water molecules.
The weight of an individual atom is represented by its atomic weight. The (rounded) atomic weight of hydrogen (H) is 1, oxygen (O) is 16, nitrogen (N) is 14, and carbon (C) is 12.
The weight of a molecule is determined by summing the atomic weights of its atoms. A water molecule (H2O) has a molecular weight of 18 (1 + 1 + 16). Free nitrogen (N2) has a molecular weight of 28, and an oxygen molecule (O2) has an atomic weight of 32. Therefore, a water molecule is lighter than either a nitrogen or an oxygen molecule.
Any fixed volume of a gas at constant pressure and temperature has the same number of molecules. It does not matter what the gas is — the same number of molecules will exist in that volume.
To make a given volume of air moister, we need to add water vapor molecules to the volume. To add water molecules to the volume, we must remove other molecules to conserve the total number of molecules in the volume.
Dry air consists mostly of nitrogen and oxygen molecules, which weigh more than water molecules. This means that when a given volume of air is made more moist by adding water molecules, heavier molecules are replaced with lighter molecules. Therefore, moist air is lighter than dry air if both are at the same temperature and pressure.