I have seen articles on the concept of using weight based generation systems as a means of energy storage, wherein the weight is lifted during times of excess and released during peak demands. But if I recall, none of them ended up being cost competitive to other means of off-peak energy storage, such as pumped-hydro storage (which as others have pointed out is in fact gravity based) or now, compressed air enery storage (CAES) systems. CAES is only now showing its viability, I have a client doing that right now in small (relative to utility scale) "plant peaker" units in the <1MW range for production facilities that need to avoid peak demand penalties or have reliable backup power. It's pretty interesting.
But in no way can there be a pure "gravity generator" that is not associated with storage of energy produced elsewhere, because gravity always sucks and until that is overcome, it always means more energy input than output. Then if someone were to solve the "gravity always sucks" concept, our overall need for energy in transportation would be so diminished that simple solar systems could give us everything we need.
"You measure the size of the accomplishment by the obstacles you had to overcome to reach your goals" -- Booker T. Washington