The air’s weight is mostly canceled

The scale would register close to the weight of the plastic bag itself, not the bag’s mass plus all the air trapped inside it. The reason is buoyancy: surrounding air pushes upward on the inflated bag, just as water pushes upward on a floating object.

A loosely inflated bag contains air at nearly the same temperature and pressure as the room. That air has nearly the same density as the air the bag pushes aside. So the trapped air’s downward pull is almost balanced by the upward buoyant force from the displaced room air.

Why the reading is not an exact cancellation

A sealed bag may be slightly stretched, leaving its interior pressure a little higher than the room’s. Its air can then be denser than the air it displaces, producing a small extra downward force. The plastic itself also has weight, and the bag’s shape affects how much outside air it displaces.

So a highly sensitive scale might detect a difference from the empty bag’s reading, but the key result is counterintuitive: air can add mass inside the bag without adding an equal amount to the scale reading, because the surrounding atmosphere is already supporting it from below.