"The pull of gravity" is not a source of energy. When the weight rises in the Earth's gravitational field energy must be supplied.
Thinking about it more, yea, fair point. When water loses energy and freezes, it expands, that expansion could lift a weight. Is this not a similar change in molecular structure doing a similar thing? Where is the input of energy lifting this weight.
No. When you apply pressure on ice it becomes liquid. In other words: water doesn't lift things by freezing if that requires an amount of energy larger than what is needed to change state.