The term weathering means the effect of weather over time on natural and man-made surfaces, but it is used as a technical term for processes distinct from erosion, i.e., distinct from the physical removal of substance through the pressure of wind and water flow. Rather weathering refers to chemical and biological processes.
Some steps in the Earth's carbonate-silicate cycle (a cycle that moves carbon from the atmosphere into water, then into the interior of the planet, then back into the atmosphere, over a geological timescale) are such weathering, e.g., the chemical effect of air and rain on exposed rock. It is believed that an increase in weathering from an increase in temperature is negative feedback to a warming climate, but at too slow a rate (millions of years) to be of much interest for 21st century issues.
For long-term geophysical modeling, the rate of weathering can be crucial, with the limiting mechanism is a factor. Some terms:
I'm not sure these are mutually exclusive.
The term space weathering is used for objects in space, e.g., from meteorite/micro-meteorite impacts, cosmic rays and stellar winds.
Weathering can be a major actor in atmosphere formation, which may include a period of rapid weathering. Also, depending on the situation, some types of weathering can serve as a stabilizing influence on a relatively stable atmosphere, such as the carbonate-silicate cycle mentioned above. Models of the formation of planet surfaces and atmosphere include weathering. So do models aimed at suggesting biosignatures.