Gas molecules move very fast and tend to mix more than they tend to settle due to gravity and density. Similar to what happens inside any bottle of liquor. Alcohol is lighter than water but it doesn't float on top, it stays mixed in. The water and the Alcohol mix naturally in part due to their shape and in larger part, due to their charges. Gases aren't quite the same as what happens with water mixing with alcohol, but the effect is similar. Water tends to mix into the atmosphere more than it wants to float above it and the high speed of atmospheric molecules tends to keep the atmosphere well mixed.
The more important factor regarding water vapor in atmosphere is temperature. Water can both evaporate into air and condense out of it and it tends to do both at the same time to some degree, leaning towards an equilibrium based on the specific circumstances. As air gets warmer it can hold more water vapor. Surprisingly more. Every 1 degree c, the atmosphere can hold as much as 6% more water vapor, so, ballpark, every 11 or 12 degrees in temperature change doubles the amount of water the atmosphere can hold. A typical summer day, provided it's humid heat, not dry heat, the air you're breathing is over 2% water.
The other thing that happens to warm air is that it's lighter than the cold air above it. This lighter air wants to rise and as it rises it cools, and as it cools it can no longer hold all that water vapor, so the water vapor tends to form tiny drops of water or bits of ice, which begin to fall towards the earth, but quite slowly, and remember, they are falling in an updraft of rising warm air, which creates the effect of clouds appearing to hover in the sky, when it's usually a combination of slowly falling ice crystals (which fall about as fast as very light fluffy feathers), and an updraft.
Pictures of warm air rising added
Water vapor in the atmosphere is transparent. It can only be seen as clouds as it condenses out of the atmosphere. (Same with fog). The mass of the individual molecules isn't very important.
As to the size of the gas molecules, that's not important either, not in a gaseous state. The standard atmospheric formula, P1V1/K1=P2V2/K2 doesn't take into account molecular size. Now for liquid or gas, molecular size matters.
You also seem to have the wrong size for your molecules, maybe you took an individual Nitrogen atom. A water molecule is one of the smaller molecules, because hydrogen is so small and tightly bound to the Oxygen. It's about 2.75 angstroms. A Nitrogen Molecule (N2) is about 3 angstroms.
Water is also polar, which helps it stay liquid at higher temperatures because the lightly negative charge on the O tends to bind with the H molecules on neighboring water molecules. Nitrogen doesn't do that, so it only becomes a liquid at very cold temperatures and despite being a heavier molecule than water (by a fair bit, 28 to 18), liquid nitrogen is about 81% as dense as liquid water. It doesn't fit as tightly together. (see 2 pictures below). The 2nd one doesn't have Nitrogen, but Nitrogen is actually a slightly larger molecule than Oxygen, which as you see, Oxygen is slightly larger than water. Water is both smaller and it fits together more neatly, so it's surprisingly dense compared to what you might expect looking at it's atomic weight.
All that said, to your question, are lighter gas molecules affected by gravity, The answer, I believe is yes, but it's a very very minor factor. Wind, mixing and chemical interactions like evaporating and condensing are larger factors. Ozone, for example is quite a heavy molecule, but it's formed and broken down high in the atmosphere long before it can fall to the earth due to gravity. CO2 is a heavy gas but the atmosphere mixes enough that it has no problem providing plants high on mountains all the CO2 they need.