When you pull the cup out of the water with the opening under the water, the normal behavior of the water is to flow until it is level. This means the water within the cup will want to have a level which is equal to that outside the cup. But by pulling the cup upward you are opening a void near the base of the cup which cannot fill with air, the base being solid material (as it must to keep water in when upright).
Because that void cannot fill with air it starts to pull a partial vacuum against atmospheric pressure, forcing some amount of water into the cup and raising the water level compared to outside. The force required to raise this water is extra force required to lift the cup, making it feel as if the cup is heavier or it “hugs the water” (an interesting way to describe it).
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