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As an adjective "heavy" reffers to the weight of an object. Weight of an object on the Earth surface is the force of gravitation of earth on the mass of an object which can be formulated as:
Weight = mass x acceleration due to gravity of earth
Fg = m x g
where, g is a constant number therefore the higher the mass, the higher the weight.
If you have two containers of equal size and you fill up both of them with water and air, the container filled up with water will be heavier as both containers have the same volume but the density of water is higher than the density of air, therefore the mass of water is higher than the mass of air.
If you take the same containers, and this time fill the second container with pressurized air to the point where the mass of the air will exceed the mass of water in the other container, then you will have a container full with air under very high pressure which will be heavier than the container filled with water. Usually at very high pressure the oxygen and nitrogen in the air will condense into liquid state so you will basically have liquids in both containers.
For the concepts of gravity, mass and weight check the web page below, the weight and mass formula is pretty much at the bottom of the page:
Hope this helps,
Have a great day!