Until the 17th century, this question would have been thought ludicrous. Air was the symbol of "nothingness" and obviously carried no weight. If it had any weight, people would be able to feel it.
Then came Galileo Galilei, who proved through experimentation that air does have weight. Today we know that the weight of the entire atmosphere is some 5.1 x 1015 tons, and that the weight of the air pressing down upon our bodies every second is about 10 tons. Only because of a wonderfully complex system in which our bodies create internal pressure equal to this external pressure do we not feel the weight of the atmosphere bearing down upon us.
Furthermore, the atmosphere is not equally dense at all locations. Cold air is denser than hot air. When air is heated, it expands and weighs less per volume than colder air. For this reason, hot air rises. This is the principle behind aerostats such as hot-air balloons (Helium balloons, such as blimps, work on a related principle, in that helium gas is lighter than the surrounding oxygen).
These facts are crucial to our existence on Earth. As the sun warms the atmosphere, hot air streams upwards in columns at different points on globe, while streams of cold air coming in from the sides replace it. This atmospheric movement generates wind that carries rain clouds from their point of origin over the oceans towards inhabited lands.
Furthermore, the cloud formation also relies on the movement of air. As low-density, hot air rises, vast quantities of water evaporate from the oceans, seas and lakes. The vapor ascends until it reaches higher levels where the temperature is lower. When the water-laden hot air meets the cold upper layers, it stops rising and condenses from its gaseous state to form a cloud. When the cloud meets a layer of even colder air, more and more gas turns into the liquid, which eventually forms droplets that fall to earth as rain.
Why do clouds release their water in steady streams of rain, rather than in single burst (which could result in flooding and damage)? The explanation lies in the fascinatingly complex system of changing temperatures, which causes part of the cloud to remain lightweight and aloft in its passage across the skies, while other parts condense and get heavier until they release their water as rain.
Another important question: Before Galileo made his significant discovery, how would the Torah Sages living 2,000 years ago have answered the question: How heavy is air and what does that mean in terms of the quantity of rain?
The Torah gives a simple, direct answer in a verse describing the wonders of creation: "He makes a weight for the wind, and metes out the waters by measure ..." (Job 28:25).
The great Biblical commentator, Rabbi Meir Lob Weiser (known as the Malbim), pointed out the obvious meaning of this verse: "He makes a weight for the wind" - The element air has weight and mass, which causes vapor to reach the clouds, due to the lower stratum of air, which is heavier than the lighter vapors. Because of this: "He metes out the waters by measure" – Hashem measures how much water stays in the clouds and how much drops down, not enough to flood the Earth.