According to the Boyle law, for the same amount of gas at a certain temperature, the pressure varies inversely with the volume. When we invert the bottle, the down displacement of water expands the air contained in the top, reducing its pressure due to the volume increase. This pressure reduction allows that the paper can sustain the weight of the water. Even so, there exists also the influence of the superficial tension that also helps the paper. The "Science Home" website has several simple experiments that can help you understand these two science phenomenon: Pressure and superficial tension. Don't forget, try the science at home!