Question

Does gravity really exist?

Answer 1

Try doing an experiment: Grab something heavy. Lift it. Feel its weight. Feel the force pulling it down. How we explain that force (talking about things like a spin-2 symmetric tensor field that couples universally and minimally to all matter fields, such that the interaction can be reinterpreted as geometric curvature) is another matter. It can be very interesting if you are into theoretical physics, and it remains one of the great unfinished projects of science. But whatever the explanation is, it does not change the fact that when you lift something heavy, gravity pulls it down with a very tangible force that you experience first-hand.

Einstein's special relativity is, well... a special case, of General Relativity in which it assumes that effect of gravity is negligible. In the same way, Newton's laws of motion is a special case of special relativity, where the motion of the body is much less than the speed of light.

Also, according to Einstein, gravity was not a force. Rather it was the effect of the bending of space-time.