This is an extension of the question if a cargo load of birds take to the wing would a flying aircraft weigh less, or no change.
In this month's edition of NTVN, the Physics Journal for members of the Dutch Society of Physicists, atmospheric scientist Peter Siegmund and geophysicist Laslo Evers report on such measurements. Using an array of microbarometers laid out at surface, they obtained transient pressure readings from flying airplanes in line with the Kutta-Zhukowsky description of flight. They managed not only to detect airplanes and determine their position, the measurements even allowed them to weigh the airplanes in full flight
How Airplanes Fly - The Real Story (With Experimental Verification!) | Science 2.0
You could request a copy of the scientific paper here, probably cost.
https://www.nnv.nl/en/english-home/