According to Archimedes’ law (also known as the law of buoyancy), an object immersed in a liquid or gas will experience an upward buoyant force equal to the gravity of the liquid or gas displaced by the object. Specifically, after the balloon is filled with a lower-density gas, the volume expands to displace the air, and the weight of the displaced air is the buoyancy force on the balloon.
Since low-density air is lighter than air of the same volume, even with the weight of the balloon skin, the gravity on the balloon as a whole is lighter. As a result, the buoyancy force is greater than the gravity force, and the balloon floats up, and then flies higher and higher.