I (like many people) have had this idea an energy storage mechanism. Unfortunately gravity batteries have an extremely low energy density for weight [1] or volume and so are only really a valid choice for something that operates at the scale of a hydroelectric dam.
Heat batteries make more sense for energy storage at a household level, whether it's heating or cooling. They're smaller, can require almost no maintenance and have a much higher energy density.
[1] https://en.wikipedia.org/wiki/Energy_density#Energy_densitie...