There are some things that are so obvious that they don't need to be proven to exist. Gravity is one of them.
What you might be really wanting to know is if gravity has been modeled; so that we can describe how it works and why. The answer to that one is...maybe.
There are two competing models: quantum gravity and the general theory of relativity. Although there are overwhelming observations and tests to validate the GTOR, there is still some reluctance by some physicists to claim that the GTOR is the definitive model.
That is, some are still clinging to the concept that gravity, like the other three fundamental forces, also have a quantum mediator particle that carries the gravity force. But there have been no tests or observations to confirm this. That quantum mediator, the graviton, has yet to be found.