Answer:
Because its made of particles
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Because it consists of matter. One cubit meter of air weighs about 1 and a 1/4 kilo's. Try this experiment. Have an empty can with a scew lid. Light a piece of paper and put it in the can then quickly tighten down the scew cap. The fire will burn up all the air in the can. This will cause a partial vacuum inside the can. You will then see that the air on the outside of the can trying to replace the missing air. It will do this by crushing the can to the amount of air lost inside the can.This then proves that air has weight.
You may ask why does not the outside air crush us as the only air we have is in our lungs? Our body is full of air and it equals the same pressure as the outside air ballancing everything.