The curvature of spacetime (not just space) is responsible for gravity. Literally, near heavy objects, the “future direction” points slightly down. So anything that moves forward in time will find its trajectory pointing down slightly. This takes the form of downward acceleration.

Is gravity caused by space-time?

Gravity is the curvature of spacetime

Gravity is the curvature of the universe, caused by massive bodies, which determines the path that objects travel. That curvature is dynamical, moving as those objects move. In Einstein's view of the world, gravity is the curvature of spacetime caused by massive objects.

How does spacetime affect gravity?

Gravitational time dilation occurs because objects with a lot of mass create a strong gravitational field. The gravitational field is really a curving of space and time. The stronger the gravity, the more spacetime curves, and the slower time itself proceeds.