That's false. Visibility has nothing to do with weight.
Carbon Monoxide, Carbon Dioxide, Hydrogen Sulfide, Nitrogen, Oxygen, Methane, water vapor, and a bunch of other gases are invisible, but they all have plenty of weight.
Air is invisible. If your bedroom is, say, 12-ft long, 10-ft wide, and 7-ft high, then the air inside your room weighs around 65 pounds !