The acceleration of the expansion of the universe is currently attributed to a phenomenon known as dark energy. While gravity does indeed play a role in the evolution of the universe, its influence alone cannot account for the observed acceleration.
According to our current understanding, dark energy is a hypothetical form of energy that permeates space and exerts a negative pressure. This negative pressure counteracts the attractive force of gravity, leading to an acceleration in the expansion of the universe. The exact nature of dark energy is still not well understood, and it remains an active area of research in cosmology.
The weakening of gravitational pull you mentioned, as the distances between objects increase, is a valid observation. However, on cosmic scales, the effect of gravity becomes relatively weaker compared to the influence of dark energy. As the universe expands, the gravitational attraction between matter does decrease due to increased distances, but the accelerating expansion driven by dark energy dominates over this effect.
It's important to note that the understanding of dark energy and its role in the acceleration of the universe is still an active field of research. Scientists are continually gathering observations and developing theoretical models to better comprehend this phenomenon and its implications for the evolution of the cosmos.