Water Vapour is never the same density as the air in which it coexists. This by virtue of the fact that although water vapour may be in effect a gas the water molecules are still larger and heavier than the component gases of "Air". If it were of the same density we wouldn't be having this discussion and nobody would have to remember anything about adiabatic lapse-rates to calculate cloud base heights etc..
A parcel, or rather volume, of air, if moist, contains water vapour in gaseous form which exerts its own vapour pressure (this is the key to the whole subject). This results in a certain amount of air being displaced out of the volume in question, e.g. 1 cubic metre. Therefore the remaining AIR in this volume is less and as a result is less dense than if there were no water vapour present.
Warm, moist air is less dense than cold dry air. This causes all the problems with engine power losses in warm, high altitude environments because the weight (direct result of molecular density) of the fuel-air mixture is upset. Remember that it is the weight of the charge, not the volume, that enters the combustion chamber that is important.
Ranting again....
