Yes, air does have weight! All of the air on the entire atmosphere weighs about 5 million billion tons!!!!! 1 ton is 200 pounds! It may not seem like it, but air does have weight.
for he views the ends of the earth
and sees everything under the heavens.
25 When he established the force of the wind
and measured out the waters,
26 when he made a decree for the rain
and a path for the thunderstorm,
27 then he looked at wisdom and appraised it;
he confirmed it and tested it
Job 28:24-27