Hovering bug

Liquids have the property of surface tension, which allows phenomena like mosquito eggs and water striders on water, the formation of round droplets, and water dripping off a waxy surface (like a leaf).

All liquids have some attractive force between their constituent molecules. When left alone, the shape that a surface of water assumes will be the one that has no net force of attraction between its molecules.

Therefore, any alteration to the shape of the surface will bring the water into an arrangement that has a greater force of attraction between molecules. This increase in inter-molecular force can counteract whatever force is acting to deform the water.

In the case of a water bug, its feet pushing down on the water causes a deformation in shape (increasing the intermolecular attractive forces) which is counteracted by the water molecules attempting to resume their preferred, force minimizing shape.

In the case of the water droplet, because there is no deforming force, there are no asymmetries in any direction. The surface simply assumes the shape that has minimum surface area for the given volume of water, which is a sphere. Thus, both phenomena can be explained by surface tension.

The other two phenomena about floating boats, and weight reduction in water seem related, but they are explained instead by buoyancy. The densities of water and ices have nothing to do with the bug's ability to float.