Your comment is a mixture of the irrelevant and the incorrect.
First, you’re mistaken about the robustness of batteries. Batteries tend to have a very short lifetime, measured in months to years, and they can typically only be recharged a few hundred times. Generators have longer lifetimes, measured in generations to centuries. Batteries are usually a lot cheaper than generators, so it might make sense, as you say, to just replace the batteries a few times. But how much does a 100mW generator cost? Amazon is selling an “X Factor” brand 3000mW generator along with accessories for US$17.56, so I suspect that the retail cost of a 100mW generator would be about US$1. (Little 1-watt brushless DC motors do cost about US$1 to US$3. I can’t find any 0.1-watt DC motors.) By comparison, the retail cost of an 800mAh AAA NiMH battery (3700 J, 1000 charges, thus lifetime about 3–5 years, Tenergy Centura brand) is about US$1.50 to US$2.
Second, it is incorrect to say, “A lifted weight stores a miniscule amount of energy compared to a battery,” except according to irrelevant figures of merit. Batteries do indeed have orders of magnitude higher energy density per kilogram and per liter, about 400kJ/kg and 1MJ/ℓ, while a bag of sand that has been lifted two meters only stores 20 J/kg and something like 20 J/ℓ. But those are not relevant figures of merit here. The target audience has tens of thousands of liters of available storage space, even in the worst slums, and can store tons of material, and the target application only needs to store 120 J. Reducing the weight of the stored energy from 6 kg and 6 ℓ down to 300mg and 0.12 mℓ (or, more realistically, 4g and 2mℓ, since you need to store more than 20' of energy) is not needed to replace a kerosene lamp; it provides you with a flashlight. Not to say that flashlights and solar lights aren’t useful, but if this is cheaper than a flashlight, maybe it’s useful anyway. Solar lights and rechargeable flashlights cost about US$6 to US$10 at retail today, which is a significant amount of money to a lot of people.
It’s true but irrelevant to say that lifting a weight by hand is not particularly thermodynamically efficient. It’s incorrect (but still irrelevant!) to say that solar lights are more thermodynamically efficient. Lifting weight is about 25% efficient, due to the inefficiency of your own muscles. (Generators are typically better than 90% thermodynamically efficient.) This is substantially more thermodynamically efficient than solar lights, which lose 85% of the sunlight on input and another 50% or so in the battery. If you can get the energy from somewhere else, rather than muscle power, then the weight is many times more thermodynamically efficient.
The efficiency question is irrelevant because we’re talking about 120 joules of energy for 20 minutes of light, which is an amount of energy that costs US$0.000003 if you have an actual power grid, or 0.03 grams of carbohydrate if you’re powering your 25%-efficient muscles (between one and two grains of rice). The only people who worry about conserving the energy in individual grains of rice are people currently experiencing a famine, mentally insane people, and commenters on Hacker News.
The one thing in your comment that might be true and relevant is the statement that solar lights are cheaper to make, because we don’t know how much the final retail cost of these Gravitylight gizmos will be. However, it seems implausible that they are many times cheaper to make. It seems likely that the vast majority of the cost in either case will be non-electromechanical components like the plastic housing, the gear train, glass or plastic to protect the solar cells, marketing, and so on, so the two solutions are likely to be almost exactly equal in cost. One will be portable but need to be left out in the yard to charge; the other will be heavy and nonportable, but you’ll be able to charge it in the middle of the night.