> Generally speaking, when we lift matter high above, we get some of the used energy back when it falls back down.
> Where is the energy stored in the meantime?
Potential energy in a gravity well is negative. The "zero" point is the limit when you get far away from all gravitational bodies. The better question is: Where does the kinetic energy come from when you descend down the gravity well in the first place?
The answer is mass. All potential energy is ultimately realized as a change in mass, equal to the famous `mass_difference * speed_of_light^2`.
As the body falls down the gravity well, it gains kinetic energy and loses mass.
When atoms bind together in an exothermic reaction, their final state is bound more tightly than their initial state. They released some energy in the form of molecular-scale kinetic energy (ie, heat), and they have lost mass.
When atoms change configuration in an endothermic reaction, their final state is bound less tightly than their initial state. Some energy was required to push them up to that higher-energy state (sometimes in the form of heat), and they have gained mass.
When light nuclei fuse together, their final state is more tightly bound than their initial state. They released some energy in the form of atomic-scale kinetic energy (ie, heat) and a photon, and they have lost mass.
Ironically, when very heavy nuclei have fissioned, their final state is more tightly bound than their initial state. They released some energy in the form of atomic-scale kinetic energy (ie, heat) and photons, and they have lost mass.
When a spring is compressed, the molecules within the elastic material are stretched apart from one another such that their final state is less tightly bound than their initial state, and the spring has gained mass.