Surface tension is the result of an electrical attraction on the molecular level - in water it is because one end (the O side) of the H20 molecule is negatively charged, and the other end (H side) is positively charged. Adjacent molecules are then attracted, positive to negative, called hydrogen bonding in water. This sticking together is called cohesion and is why droplets form on your well waxed car - the cohesive forces are greater than the gravitational forces trying to flatten out the water.
Similarly, there are adhesive forces between a liquid and a solid, that are sometimes greater than the cohesive forces, hence capillary action. If the water in a glass were not subject to gravitation, it would climb right out of the glass and cover as much of the glass as possible. With gravity, it rises until the adhesive force and the gravitational force are balanced. Same thing with a sponge or piece of paper.
So, when you dip your paper into the water, the surface tension or surface energy, which is a form of potential energy, is overcome by the adhesive forces which draw the water up, i.e., input of kinetic energy, and increase BOTH the surface energy and the gravitational potential energy. Surface energy wants to decrease the surface area, but you are in fact increasing the surface area, therefore increasing the surface energy.
I got most of this information from “Understanding Physics” by Isaac Asimov.