This is due to friction with the air. Yes, it still has the same mass but an inflated balloon has more surface area and therefore encounters more air molecules on the way down. So this causes more friction.
Actually the same principle is used in parachuting. There’s no difference in mass between the freefall and canopy-open stages of a parachute dive. But the increase in surface area (the parachute) slows you down enough to survive the fall.
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