Density of moist air
The composition of dry air is about $78\%$ $\ce{N2}$, $21\%$ $\ce{O2}$ and $1\%$ $\ce{Ar}$.  The molecular weights of these compounds are:
$\ce{N2} = \pu{28 g/mol}$
$\ce{O2} = \pu{32 g/mol}$
$\ce{Ar} = \pu{40 g/mol}$

So, the average molecular weight of dry air is given as:  

$\pu{(0.78 * 28 g/mol) + ( 0.21 * 32 g/mol) + ( 0.01 * 40 g/mol) g/mol = 29 g/mol}$  

The molecular weight of water is only $\pu{18 g/mol}$.  

So, a molecule of air being replaced by a molecule of water results in an air molecule with an average molecular weight of $\pu{29 g/mol}$ being replaced by a water molecule having a molecular weight of only $\pu{18 g/mol}$.  

This scenario assumes a constant temperature and pressure when humidifying the air.