I dipped a sticky note in water and there was a clear difference between the water absorption in the area with glue and the one without glue. The area with glue was more damp than the one without it. I would like to know why.
I like your "why?" question. So I dig down to find out why Post-It notes stick to any surfaces, yet, when removed, it's able to post again in another place. This is my finding and it makes sense Adhesives:
Look at the back of a sticky note using an electron microscope and you'll see not a continuous film of adhesive but lots of microscopic glue bubbles, known as microcapsules, which are about 10–100 times bigger and much weaker than the glue particles you'd find lazing around on normal sticky tape. When you push a Post-it® onto a table, some of these relatively large sticky capsules cling to the surface, providing just enough adhesive force to hold the weight of the paper in the little note. Every time you attach and peel off the note, dust and dirt attach to the adhesive capsules, so they progressively lose their stickiness. But since there are so many capsules of all different sizes, a Post-it® note does go on sticking for quite a while.
I believe, when you dipped your sticky note in water, these microcapsules filled with water, which would be a thicker layer than the water in other areas. So, gum layer area contains more water, thus, that part is actually more damp than the rest of the paper.