Why does paper bend on it's own when it gets really humid out?

The fibers of paper are held together by binders called “size”. At high relative humidities, these soften and allow the fibers to move against each other. This makes the paper lose its stiffness and go limp. This explains why the pages of a hanging calendar, for instance, no longer resist gravity and droop at the corners.

Also, the cellulose fibers of paper expand in humid conditions. Some papers are coated on one side with substances intended to modify surface qualities. These can keep that side of the paper from expanding at the same rate as the uncoated side when the paper fibers swell, so the paper will curl toward the coated side.

However, the thickness of the paper DOES play a role. The thinner the paper, the more readily it will curl.