First, the word "weathering" misleads many people. Weathering often has nothing to do with weather. Instead, it means either breaking rocks into smaller pieces or dissolving them. Weathering does not involve moving the pieces of rock. When the pieces are moved by natural forces, such as wind, water, ice, or gravity, that is erosion.
It is possible to have weathering without erosion, erosion without weathering, or both at the same time. In this photo, both are happening. The wave is carrying sand (erosion) which hits the rocks. That breaks tiny bits off the rocks (weathering), and then the wave carries them away (erosion.)