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assuming the volume of flour changes with humidity because it contains more moisture, wouldn't it also increase the weight?

Not an expert by any means though, so correct me if I'm wrong

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When flour gets wet, it sticks together to form dough. Dough can have large air pockets in it. Dry flour with a bit of humidity can also form these air pockets, albeit typically on a much smaller scale.

Whether you pack flour down or sift it through a sieve into your measuring cup can make a huge difference in the weight.

No, not at all. Volume ≠ Weight.

Another example: Some books use paper with bigger volume (so it looks thicker) but of course they are not twice as heavy suddenly.

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