The pressure inside a balloon has an inverse relationship with the thickness of the balloon in its inflated state.
This is why getting the first puff into a balloon is by far the hardest. As you inflate it more and more the thickness of the rubber decreases so its ability to compress the air to a higher pressure also decreases.
In the two balloon example you mention the smaller balloon is closer to the state where you have to put a lot of effort into initially inflating it, so the air pressure is higher, so when you open the valve the air flows from the higher pressure zone to the lower pressure one.
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