What really causes a low-pressure gradient over the top of an aerofoil? As air flows over the top of an aerofoil the pressure drops. Compared to the high / normal pressures on the underside, a pressure gradient is formed with higher pressure further above the wing. You get:

less pressure = less particles = less density 

This sketch summarizes what I know so far:



My questions are:


Does lower air density above the wing mean the air weighs less compared to the weight of the air underneath the wing? If the difference is negligible then it's OK, we can forget it.
What forces act on the air particles causing them to speed up?
This is my understanding: A combination of the shape, angle of attack and movement of the wing creates high pressure on the front side of the wing and low pressure on the back side. By front and back I mean the part that is facing the oncoming air and the part that cannot "see" the oncoming air. 

The low pressure is there because of this. This is the pressure difference which causes lift. Some lift also comes from the downdraft caused by air moving downwards at the trailing edge of the wing due to the angle of attack.

This article has a video that shows airflow over a wing.
http://www.cam.ac.uk/research/news/how-wings-really-work