As an extension of the nautical analogy, imagine a toy submarine at neutral buoyancy circling, submerged, in a bucket of water on a scale. Now replace some of the air inside the submarine with lead, but set the dive planes so it continues to circle at the same level.
The reading on the scale has to increase by the amount of lead added, but the water level in the bucket won't change. The answer seems to be that the hydrodynamic effects of the dive planes increase the dynamic pressure at the bottom of the bucket. I'd guess that the same is true for an aircraft flying in the atmosphere, even though the effect would be too small to measure.
I assume the effect would be localized as well -- after all, atmospheric pressure isn't the same everywhere to start with. Imagine a helicopter hovering above a set of truck scales.