The way I understand the process is that Bernoulli describes the manifestation of Newton 3G in the scenario of an aerofoil passing through the air (or the air passing over an aerofoil). In the case of an aircraft in unaccelerated flight, Lift=Weight and Thrust=Drag. The powerplants create the necessary thrust to propell the machine through the air (and therefore the air over the wing) this thrust is balanced (N3G) by the drag created by the aeroplane in a direction parallel to the thrust line. However, because the wing is curved, the air passing over the top creates a lower pressure than that below resulting in lift (Bernoulli). Because the aeroplane is travelling forwards, the inevitable counter balance to the lift created (3G) is felt at some distance behind the aircraft in the form of wake turbulence. I.E a weight of air equal to that of the air being displaced, rather than being directed vertically downwards is actually deflected downwards and backwards. This process is most easily seen in the form of wingtip vortices at take off and landing when induced drag is at its highest.
Then again, I only fly the things so what do I know? The smelly pilot theory has yet to be disproved...