What keeps water molecules in air from falling down? I was thinking about evaporative cooling, how the particles in water with the most velocity fly out of the water, leaving it colder. But then I thought, how come these water molecules stay in the air without falling back down to the liquid? Which begs the question, how do any water molecules in air stay in it? 
I mean, they are heavier than air. Gravitation works on them just fine, so without air in the way they would certainly fall straight down with the same velocity of any human-sized falling object. So I would guess that the air molecules in the way between them and the floor are keeping them up. But how can they do it? I assume that air molecules are keeping each other up from the ground because they have a bigger force between them (in room temperature) than water molecules do, because air is gas in room temperature. But water isn't gas in room temperature so it shouldn't have such big repulsion forces between molecules. Or maybe I'm confused? Please shed light on this. 
 A: 
I mean, they are heavier than air. 

No.  
Water is $H_2O$ which has a molecular weight of 18.
Nitrogen is $N_2$ which has a molecular weight of 28.
Oxygen is $O_2$ which has a molecular weight of 32.
Argon is $Ar$ which has an atom weight of 40.
So a water molecule has a mass that is less than that of all the significant components of air. 

But then I thought, how come these water molecules stay in the air without falling back down to the liquid?

There is a dynamic equillibrium.  When there is a body of water, with air containing water vapor above it, gas phase water molecules DO continuously condense into the liquid water.  One way to verify this is to leave a $D_2O$ bottle exposed to the air for a period of time, and look at its proton NMR spectrum before and after.  
In other words, if the liquid water is in equillibrium with moist air, the rate at which liquid water molecules enter the gas phase is equal to the rate at which gas water molecules enter the liquid phase.  If the system is out of equillibrium, net evaporation or net condensation occurs, until equillibrium is reached.  
A: First, water molecules are NOT heavier than air molecules.  Air is mostly N2 (molecular weight 28) and some O2 (molecular weight 32).  H2O has a molecular weight of only 18.  So all else being equal, you would expect water vapor in the air to rise on average.
However, at the level of individual molecules, gravity is a miniscule effect and swamped by the forces resulting from constant collisions between molecules.  Think of a gas as a large box filled maybe 10% of the way with ping-pong balls.  Now vibrate the box.  The ping-pong balls will bounce around so that on average there is more space between them when they were just a layer at the bottom of the box.
Any one ball will randomly bounce around with a unpredictable path inside the box.  Gravity is small compared the the forces of individual collisions.  The collisions add so much noise that the effect of gravity is hard to see at the micro level.  You can see the effect of gravity by looking at a the average of a large number of balls.  The noise from the collisions will average towards zero, leaving the effect of gravity more obvious.  By averaging many individual noisy data points, you increase signal to noise ratio.  At that level you will see the distribution of balls denser at the bottom than the top.  You can even write a equation for the expected average density as a function of height.  This is how gasses, including our atmosphere work.  Due to gravity, there are more molecules packed in the same volume at sea level than a mile up in the air.
Now imagine you painted one of the ping pong balls black and made it a little heavier than the others.  Would it always rest on the bottom?  No, it would bounce around like the others, although over a long term average there would be a higher probability of finding it nearer the bottom than any of the other balls.  In other words, all the bouncing forces overwhelm gravity, so you can only see gravity's effect over a large sample or over a long time.
Your water molecule in air works the same way, except that it is lighter than the other balls and therefore over a long term average is more likely to be higher than other balls.  All this bouncing around is called Brownian motion, and is proportional to the temperature of the gas molecules.
A: All of the molecules in the air are constantly colliding and rebounding off each other, which keeps them from "falling down". If they were to fall down under gravity the pressure would increase, and there would be a net force upward. This is why the pressure high up in the atmosphere is lower than at sea level.
While water doesn't BOIL at room temperature, there are still molecules in the gas phase. There's an equilibrium (vapour pressure) pressure that is a function of the ambient pressure and temperature. So the water molecules are just like any other molecules in the air.
A: In most systems that involve the evaporation of water, gravity plays an extremely minor role. We can, in most cases, ignore the effects of gravity.
What makes water boil/evaporate is the thermodynamic concept derived from the first and second law of thermodynamics.
You can read this article to find out the derivation from entropy to the Clapyeron equation.
http://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation#Derivation_from_state_postulate
$$\frac{\mathrm{d} P}{\mathrm{d} T} = \frac {\Delta{H_{vap}}}{T \Delta v}.$$
And the integral form is: 
$$\ln P = -\frac{\Delta{H_{vap}}}{R}\left(\frac{1}{T}\right)+C.$$
where $P$ is the vapor pressure at that particular temperature. 
For example, at room temperature (20C), the vapor pressure of water is about 2.3kPa. This means that water will evaporate until it reaches a partial pressure of 2.3kPa and then the water will attain 100% relative humidity. 
The driving force of this evaporation is actually thermodynamic related. Evaporation occurs in order for the system to reach thermodynamic equilibrium (the elaboration is readily available online). The explanation that "particles in water with the most velocity fly out of the water" is just an analogy to describe it in physical terms.
A: Brownian motion - the force exerted by the surrounding gas molecules is far greater than that exerted by gravity. If you were being hit constantly, from all directions, by objects about your own mass but travelling around 500 m/s gravity would not affect you all that much either.
