Why does water stay in a cup upside down?

If the weight of the water is less than the air pressure inside of the test tube.

Try this on your friends. Fill a glass to the brim with water. Place a piece of flat cardboard over the rim of the glass. Place your hand over the cardboard and invert the glass. Take you hand away and the water will remain in the glass. Air pressure again come into play here.

Try this one as well. Place a small lighted piece of paper in to an empty plastic bottle or tin can. The lighted paper will burn up the air in the container and will eventually go out. Because there is now a partial vacuum in the container the outside air pressure will try to fill the space and will gradually crush the bottle or can.