Using that same logic, you would expect all of our air to fall to the ground. Although all of the atoms are of course affected by gravity, the absolutely tiny mass, means that gravity's pull on any given atom or molecule is very very small. Because we have an atmosphere, we can imagine that most gasses have relatively similar densities to our air. Thus diffusion takes over, and the animation is probably pretty accurate. Thermal energy is more than enough to induce "Brownian motion" which means particles behave randomly.

Diffusion is the net effect of random (unbiased) collisions. In the case of gravity you have the random diffusion occurring, but now a constant pull due to gravity. Nothing opposes this gravity force so the center of mass of the particle's trajectory should rise or fall depending on the relative density of the 'smell' particles and air. If it's a gas, then it probably doesn't have a very different density, so this 'settling velocity' is quite small. The dominant methods of transport tend to be primarily convection (gust of wind), then diffusion, then settling with gravity. It's also important to keep in mind that this propensity to spread is a function of the particle's mass because the random collisions impart random amounts of momenta which are damped by the mass of the particle to tell you how it changes velocity (dv = dp/m).

Particles are affected by gravity, so you know there must be something preventing them from falling. In this case, it's air currents and the molecular motion of air. When particles are very small, random collisions with other molecules will keep them suspended in the medium. However, as the particles get bigger, their difference in density from the medium will begin to cause them to separate.

Take fine mud in water as an example. If you stir up a mixture of mud and water, you'll notice that over time the water gets less cloudy. The big particles settle out very quickly (like a rock), whereas the very fine particles (like silt) seem to remain mixed in the water for a long time.

With smells, you are often dealing with small molecules, which are very light by comparison to most things we deal with. It's very easy for these molecules to remain suspended in air, because of the collisions with other air molecules and the currents in the air I mentioned earlier.

Technically, yes, the molecules that diffuse through the air that we detect as smell are just as affected by gravity as everything else. However, these molecules aren't just moving through a vacuum; they're diffusing through a gas, and since the gas has a temperature, the molecules of the gas are continuously jostling around because of thermal excitations. It turns out that the bouncing around of molecules due to thermal excitations is incredibly stronger than the effect of gravity on the molecules, so gravity is basically negligible, and the particles essentially diffuse out in a spherical pattern (although, bear in mind that on large scaled, gases as a whole do fall to the ground - that's what prevents the atmosphere from just flying away from the Earth!)

You can think of the scent molecules as being even much smaller andlighter than the lightest feather, so the air currents are muchstronger than the pull of gravity on such light-weight things asmolecules.

Science teaching is such an important job. Keep asking questions!

They are particles, but these particles are in a gaseous state, and, just like any other molecule in the air, they are buoyed up by collisions with other molecules, and otherwise vibrating so fast that gravity only affects them on a very large scale (I believe that air molecules move around at about the speed of sound, which is why sound travels at the speed that it does). Just as if you fired a bullet into the air at a thousand feet per second, it would take a while for it to come back down, and if the bullet were as light as the air molecules themselves, then it might never hit the ground because it would be spending all of its time bouncing off of other air molecules (and maybe bouncing off of the ground).

On the Moon, most of these particles would fall to the surface (those that aren't moving fast enough to escape the weak lunar gravity entirely and float off into space, which eventually all of them would because the energy to get going that fast is available in sunlight - this is why the moon doesn't have much of an atmosphere).