To maintain level flight, a plane has to generate lift equal to its weight. It generates lift by forcing a mass of air down. More mass means more air disturbed.
When people explain flight through Bournoulli or whatever, they tend to forget Newton's basic laws, which really are the simplest way to understand flight. It won't make you an aerospace engineer, though.
Not quite. Outside of ground effect, a downward force is applied to the air mass around the aircraft, resulting in lift on the aircraft. IIUC, this results in compressed, high pressure air below the plane and low pressure air above it. The result of that is a pair of vortices roughly centered on the plane's wingtips. These vortices themselves are Somehow Important to the whole thing. Anyway, you can see the deal when a plane flies close to a cloud top.[1]
In ground effect (i.e. the aircraft is flying within roughly one wingspan of the ground), the proximity of the ground blocks the formation of the wingtip vortices (?) and greatly enhances the efficiency of lift production (by some form of magic, AFAIK).
You need to sum craft weight and lift when applying Newton's laws in figuring downward pressure, more lift -> less ground pressure across all craft weight.