What type of rock is formed by weathering and layering?

A rather simplified answer: Weathered rocks are broken down by ice, rain and wind, into smaller rocks, pebbles, sand, and silt. When the lighter sand and silt is carried by rivers, etc. and reaches the sea, it may form a layer on the sea bed. If the layer is placed under tremendous pressure, and is mainly of sand, sandstone is formed (over many eons). If mainly silt, slate is formed.