Does air pressure change with humidity?
As humidity increases pressure decreases. Since water vapor is less dense than dry air if both have the same temperature, the addition of water vapor decreases the overall density of the air and lowers its pressure.
Please do not read the other provided answer as it is completely incorrect.
Water is 2 hydrogen atoms and 1 oxygen atom. The atomic mass of hydrogen is approximately 1. The atomic mass of oxygen is approximately 16. That totals 18 approximately.
The main constituent of the atmosphere is molecular Nitrogen, in other words 2 nitrogen atoms. The atomic mass of each Nitrogen atom is approximately 14. Therefore the total is 28.
That is the math of it, water is lighter than nitrogen. Increased humidity (absolute humidity not relative humidity) will always lower air pressure.
Furthermore the 2nd main constituent of air is molecular oxygen. 2 oxygen atoms have a molecular mass of 32. Much higher than that of water vapor.
Another way to look at it is of course density. The reason that water vapor is less dense than dry air is because of the mass of the molecules. Water vapor molecules have less mass and the formula for density is mass /volume. The higher the mass the higher the density for a given volume. That is also why, as Truong-Son state, the temperature has to remain constant. Temperature is proportional to volume according to Charles's Law.