When the weather plays a part in eroding rocks, this is known as weathering. Different types of weather will break down rocks in a different way.
Rain has two ways of breaking down rocks. Firstly by the process of erosion. When it rains a lot, rivers will fill up with water and often flow faster. The more water a river holds, the more sediment it is able to carry. This sediment hits the rocky banks of the river and will cause erosion.
The second way rain can break down rock is by acid rain. Acid rain occurs when the rain has high levels of hydrogen ions, having a harmful effect on rocks.
This picture demonstrates the effect that acid rain can have on rock.
Ice plays a particularly destructive part in breaking down rocks. When water gets into a crack in the rock and freezes, the water will expand. When the ice expands too much for the crack in the rock to handle, more of the rock will crack and fall away.
Wind will cause erosion by blowing bits of sediment such as small rocks and sand, into larger rock. This constant process over time will gradually begin to wear the rock away. If a rock formation has softer rock underneath harder rock, the soft rock will erode first, possibly making the harder rock crack and fall as well.