It's an idea that's been played with a few times, but there are many energy loss points in such a system, as well as logistics for keeping the "stack" from falling over. The best so far is pumping water up to an artificial lake, but that's still not very efficient.

The energy math doesn't make sense for grid scale applications with solid objects.

https://youtu.be/iGGOjD_OtAM

However if you can get water between two places it can work quite well. You need to live close to a big change in altitude and do a bit of geoengineering to create the upper and lower reservoirs, which can be destructive to local ecology, but not as much as a dam.

https://en.m.wikipedia.org/wiki/Pumped-storage_hydroelectricity

You can also use pumped air underwater with higher energy losses than pumped storage hydro because of compatibility of air.

https://electricalindustry.ca/changing-scenes/1785-world-s-first-utility-scale-underwater-compressed-air-energy-storage-system-activated-in-lake-ontario/

1 Watt is the equivalent of moving 1Kg 1 metre in 1 second.

If you want a kilowatt - you need to move 1,000Kg 1 metre in 1 second. Or, I guess, 1Kg a Km.

Plug the numbers together and you'll see that you need a massive physical load and a huge distance in order to store a useful amount of energy.

We have, pump storage hydropower: https://old.reddit.com/r/askscience/comments/chm70g/askscience_ama_series_were_from_the_pacific/

Basically they store water up high to act as a battery. Some combine this with a solar lens and turbine (can be sourced from old tvs, it'sa Fresnel lens for a solar death ray) and boil the water with the sun/ray to get it to evaporate and then condensate in the elevated position.

Potential energy (in joules) is mass (in g) times height (in meters) times 9.8 m/s^2 .

So in order to store the 30 kWh per day that the typical American house uses, you'd need to convert the 30 kWh into 108,000,000 joules, and divide by 9.8, to determine how you'd want to store that energy. You'd need the height times mass to be about 11 million. So do you take a 1500 kg weight (about the weight of a Toyota Camry) and raise it about 7.3 meters (about 2 stories in a typical residential home)? (this is wrong, it's only 0.001 as much as the energy needed, see edit below)

And if that's only one day's worth of energy, how would you store a month's worth? Or the 3800kwh (13.68 x 10^9 joules) discussed in the article?

At that point, we're talking about raising 10 Camrys 93 meters into the air, just for one household. Without accounting for the lost energy and inefficiencies in the charging/discharging cycle.

Chemical energy is way easier to store.

Edit: whoops I was off by using grams instead of kg. It actually needs to be 1000 times the weight or 1000 the height. The two story Camry is around a tablet battery's worth of storage, not very much at all.

It's usually called hydroelectric and implemented with dams and turbines.

Adamsomething covered this a while ago.