Air pressure and density primarily affect the physics or dynamic movements of air. This includes rising warm air and sinking cold air. As you can see in the list below, air pressure and density affects weather by controlling the flow of air, the transportation of heat and moisture and cooling and warming of he atmosphere through expansional cooling and compressional warming.
1. Air Pressure differences affect the flow of air (wind). Because air naturally flows from areas of high pressure to low pressure, pressure differences over an area (pressure gradient) causes air flow or wind. Air pressure is the main cause of localized and planetary scale wind.