Counterbalances are in use all over the place, look at lifts (/elevators) if they didn't have the weights they'd need much much more energy to move the system. Almost everything that works with weights+heights will have some kind of counterbalance system.

Hydroelectric energy storage is one example that is hugely successful, albeit requiring geography to help. We also use water towers in some places to maintain pressure in pipes with the hydraulic head.

On a smaller scale, it's more space efficient to use weights to store rotating energy as a flywheel.

That said, stored energy in a system isn't always a desirable property, generally it means more careful designs are needed so that the system defaults to safe.

In order to store any significant energy, you'd need great heights or giant mass. Both rather impractical.

That said, one of the oldest energy captures is a watermill. It's powered by gravity.

There are many mechanisms powered by the Huygens weight drive + a governor, for example many clocks.

https://en.m.wikipedia.org/wiki/Maintaining_power