Please do the maths on "lifting weights up a tall tower.

Actually no, I’ll do it for you.

Let’s raise a metric ton 10 storeys. A storey is about 3 meters, making that 1000kg going 30 meters up. Mass (1000kg) x g (9.81m/s² ≈ 10m/s²) x height (30m) is about 300,000 joules of energy. We don’t use joules much, but they are the amount of energy you use is you draw 1w for 1 second. 300,000Ws. 3,600 seconds in an hour, so 83Wh.

Not kWh, Wh. You might run your TV for an hour.

You’d need to lift 100 tons 100 storeys to get it to kWh. 83kWh. A car battery worth of storage.

This is the reason pumped-hydro storage is a thing. To make lifting a mass a decent energy storage solution, you need a lot of mass. About the order of one lake of water. One plant I visited in Scotland has a reservoir of 10 million tons of water elevated 400 meters, to give it 7GWh of storage. That’s a fairly small one, and 36 men died building it back in the 50s/60s.

Gravity storage needs BIG numbers.