When the mug is under the water upward buoyant force acting on the mug reduces the weight of the mug. Due to that mug appears lighter when it is under the water. Or in other words can be explained as under the water it experiences upward buoyant force that cancels the gravitational force acting on the mug and it weighs lighter. When the mug is taken outside there is no other force to cancel or reduce gravitational force acting on the mug and it weighs much more.