What we call "air" is actually a mixture of several different gasses. Air is roughly 78% Nitrogen and 21% Oxygen. The remaining 1% composed of Argon, Neon, Carbon Dioxide, Helium, Methane, Krypton, and Hydrogen. All of the atoms of these gasses are constantly flying around slamming into each other and mixing up the whole atmosphere. Although Oxygen is slightly more dense (1.429 Kg/m³) than Nitrogen (1.2506 Kg/ m³), they do not separate like oil and water because weather conditions like wind keep them mixed up. These densities are at Standard Temperature and Pressure (0^oC (273.15 K, 32^oF) and 1 atm)

When we say that air is thinner at altitude, there is a smaller amount of ALL the gas particles in a given volume. This is because air pressure decreases as we get further away from the surface of the earth because there are less particles of air pushing down on it.

Think of the atmosphere as a giant "ocean" of air. When you swim deeper in the ocean, the pressure gets greater because there is more water on top of you. The same thing happens in the atmosphere.

Air is a mixture of gases, mostly nitrogen and oxygen
78.1% nitrogen
20.9% oxygen
0.9% argon
0.1% other gases (like carbon dioxide)

Air is well mixed, so we do not usually talk about oxygen being lighter or heavier than air. Helium, on the other hand, is much lighter than air (nitrogen and oxygen), so that is why a helium-filled balloon goes up.

At higher altitudes, the air is thinner (less atoms in the same volume), but the relative amounts of nitrogen and oxygen are the same. This is true until you get about 100km (60 miles) above the surface of the earth. Above that level, light gases like helium and hydrogen are most common.

Air thins as you go up in altitude because the majority of air is held close to the earth's surface by gravity.
Great questions!

"Air is a mixture of gases, primarily nitrogen and oxygen. Oxygen is denser than both air and nitrogen, at all temperatures and pressures, but only slightly. Since they don't separate from each other, we generally don't worry which is lighter or heavier. The difference in the density of nitrogen and oxygen gas comes from their molecular weight, which is small (4 g/mol). You can account for the density of air at normal temperatures and pressures (68F, 1 atm) by adding up the weighted percentages of nitrogen, oxygen and argon. (0.1% is other gases like carbon dioxide but we'll ignore it for this calculation.)
Air = 78.08% Nitrogen + 20.95% Oxygen + .93% Argon
0.7808 (1.2506) + 0.2095 (1.4290) + 0.0093 (1.7837) = 1.292 kg/m³ which is very close to the measured 1.205 kg/m³ density of air.

Note: Standard Temperature and Pressure (0^oC (273.15 K, 32^oF) and 1 atm)

There is a common misconception that nitrogen is denser than air because when liquid nitrogen boils, the nitrogen gas pools on the floor. This isn't because the nitrogen is denser but that the cold gas (N₂) is denser than the warm gas (air) around it.

Our atmosphere is held to the earth's surface by gravity. The atmosphere is less dense at higher altitudes (which leads to lower air pressures) because the molecules feel less gravitational force. The thinner air has the same percentages of nitrogen and oxygen, but less of both. You generally don't notice that you are getting less oxygen per breath until you get 4000 ft or greater above sea level. At 5280 ft high, Denver has 17% less atmosphere than sea level so most visitors take a while to adjust.

You might think that heavier gasses (like oxygen) would be concentrated closer to sea level and lighter gasses concentrated in the upper atmosphere because their weight/densities. This would be true if there was no wind, but their differences in weight are canceled out because our atmosphere is in constant motion (wind) due to local differences in temperature. There is actually very little helium or hydrogen in our atmosphere at all - these gases are so light that, once released, they eventually drift to the top of the atmosphere where they can escape Earth's gravity off into space!

Here is an excellent summary of how air's density affects weather: