He probably stretched the left balloon before filling it, making the pressure inside less than the right, which he didn’t pre-stretch.

I think it is to do with stretching too, but I don't think he pre-stretched it I just think the more inflated balloon was stretched by inflation.

The test would be to fully inflate two balloons, half deflate one, and then connect them.

I think it's a function of the pressure of the air already in the balloon relative to the pressure required to add air to the balloon. When you blow up a balloon the first few puffs require a lot of pressure to inflate and then it becomes easier until it approaches maximum size.

That is sort of right. Basically it is a law of physics, Boyle's law. The larger balloon has a lot more space for the air particles in it to move around, meaning less pressure (to a point). The small balloon has very little space, creating a condition of higher pressure, causing the air particles to seek a larger space to move into.

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