Wind turbines use the tower to take parts to the top for maintenance. Regardless, you'd need to dramatically increase the wall thickness of the tower along with

Wind turbines use the tower to take parts to the top for maintenance. Regardless, you'd need to dramatically increase the wall thickness of the tower along with the foundation for the additional load, to the point it probably wouldn't be worth it. Bad math, let's say we can use a lead weight 2 meters in diameter, 3 meters tall (107,000 kg) with 120 meters of drop available. All of that gets us 35 kWh, or 0.035 megawatt hours of energy. Compared to a 2 MW turbine, it's a negligably small amount of stored energy, even if we scaled every dimension up by a factor of 2 (getting us to 0.28 MWh).