If you're going to use weights and gravity as a storage, as many people have pointed out the best solution is water. A pelton wheel will deliver near 100% conversion of falling water into shaft power, and a force pump will deliver near 100% conversion of shaft power into lifted water.
The physics is simple: height times weight times gravity equals energy.
The problem is size. Raising 1 ton of water 1 metre stores 9810J, so to store a kWh (3,600,000J) you need to raise 1 ton 367 metres, or 367 tons 1 metre, or 36.7 tons 10 metres, or whatever combination you like. If you think your batteries are big and heavy, wait until you see pumped storage.
A ton of water is 224 Imperial gallons, or about 263 US gallons. A metre is about 39 inches, or three foot three. :-)
Normally if you have the right lay of land to make pumped storage work, you also have the right lay of land to make a conventional hydro system work. Which is why there are so few of them in the world, and why the electricity generators still waste capacity in the wee small hours.