Is the air pressure high on sunny days or cloudy days? Why? What is the general difference?

The air pressure on sunny days is high, because the content of water vapor in the air on sunny days is relatively small and the density of water vapor is smaller than that of air, so the average density of air on sunny days is larger than that on cloudy days. So the air pressure is higher on sunny days. As for the difference, it depends on the change of water vapor content in the air.