How is a improperly inflated ball going to weigh less than a properly inflated ball since air is weightless?
I don't think weighing the ball is the most accurate way to determine the pressure of air in it, but theoretically, the method will work.
Just thinking out loud, maybe the (or another) suspicion was that the ball was not regulation weight (a separate consideration from how much air is in it). Regulation football has size, weight, and pressure limits.
Air has mass, just like all matter. Compressed air at a given volume weighs more than uncompressed air at the same volume.
Air is not weightless. It.has mass
I don’t think the issue is the weight of the ball, but the fact that the surface of the ball would be softer... easier to grip.
It takes about 5 grams (about 1/6 of an ounce) of air to inflate a football to 13 psi, about the same weight as a tablespoon of water. A partially deflated ball will be one or two grams (a teaspoon of water) lighter. However, an offical football weighs between 410-450 grams (0.90 to 0.99 pounds). You cannot tell the difference between a fully and partially inflated football by weighing it.
If the guy knew the difference between pressure and weight he probably wouldn’t be a sports reporter.