Pumped hydro is by far the most commonly used utility-scale energy storage in use today. Efficiency is in the range of 70-80% so it's a lot better than compressed air in that regard, the main downside is that you just need a really large amount of water and a place to put all of it.
Lifting weights for energy storage is not really very conceptually different from pumped hydro (both store gravitational potential energy), water just happens to be vastly cheaper per ton than pretty much anything else. Concrete is something like $50 per ton and water is more like $0.50.
How about instead of pushing water up into the air, you pulled air down into the water. Build a big floating object at sea and drag it down into the water with a cable attached to a motor/generator.
I think you would have to use a vessel that could withstand underwater pressures. I imagine that would be on the expensive side, probably more expensive than the concrete blocks. And if the the vessel compresses at all, I think you loose efficiency due to the loss of buoyancy.
On a more general note, I think the issue with these novel storage methods is that even their more optimistic $/kWh targets are barely competitive with existing battery prices. And due to manufacturing scale, battery prices are expected to continue to decline. A similar thing happened in the solar market. Prices were really high, which led to a bunch of startups attempting to bring novel technologies to market (Solyndra was one of them), but once China started flexing its manufacturing muscle, PV prices dropped and the novel technologies had no hope of competing.
I wonder what it'd cost to use a waste material like slag. Slag weighs like 90% of the weight of concrete and is 10% of the price--because we basically throw it away. I guess the biggest cost would be containers to hold it. Even if the (cost container to hold slag + cost of slag) = (cost of equal weight concrete)--we're not using up concrete that could be used for things that actually need concrete. Here we just need something heavy that won't collapse when lifted. Plus, concrete releases co2 when poured. I guess co2 would have to be released to manufacture the containers--but even then...interesting thought.
Lifting weights for energy storage is not really very conceptually different from pumped hydro (both store gravitational potential energy), water just happens to be vastly cheaper per ton than pretty much anything else. Concrete is something like $50 per ton and water is more like $0.50.