Make that 1600 lb Cessna a helicopter and place both you and the heli in a jar with it hovering over you. I am sure you'll feel something then. The 1600 lb Cessna is exerting a downward force but that force is not trapped to be just above your head. Just like air within a ballon, it has room to expand sidewards, upwards and downwards. Of course the path of least resistance usually wins out...
I agree you would feel something- a LOT of wind moving around. But for a wing to create lift, what's underneath it is not a factor until you're very near the ground. I am not sure, but maybe it has something to do with the fact that air compresses easily?