Perhaps considering a helicopter might be helpful. A helicopter flies using the same principles as a fixed wing aircraft or a bird - air flowing over an aerofoil causing a reduction in pressure.
When a helicopter hovers over the sea the water is flattened out a little (excuse the bad terminology!), and small waves tend to be blown out towards the edges by the air circulation.
Isn't it true that this particular helicopter is supported by air being accelerated downwards, and the air is brought to rest by the ground (water)? So by F = m.a, there is a force on the surface of the earth.
If the helicopter was hovering inside a C5, the floor of the C5 would have to support the deceleration of the downwash air. Ditto for birds I suppose.
On a more techy note - 404 Titan - I'm not sure that the weight of aircraft is quite spread evenly over the entire earth's surface. Although the swimmers in your pool are supported by the water, which transfers their weight to all parts of the pool's floor evenly, I'm not sure it's the same for aircraft. Swimmers are floating, they displace a weight of water equal to their own weight, the displaced water spreads itself out evenly over the rest of the pool. However, heavier-than-air aircraft don't float in air, as they are supported by constantly accelerating air downwards. They don't displace a weight of air equal to their own weight, so there will be a pressure pulse under an aircraft. Stand under a 747 flying at 20' and you'll detect it, but perhaps the pressure pulse under aircraft flying at 500'+ is too spread out to be easily detected.
Cheers to all,
O8
