Both are correct.
To "weather with time" or "weather over time" suggest a gradual, continuous process. There's no exact moment at which the stone becomes "weathered."
To "weather in time" almost suggests that someone is waiting for the stone to become weathered. There is a feeling of something happening at a definite time. For example, "names carved in granite last longer than names carved in slate, but even the hardest stone will weather in time."