I say the plane in zero gravity would climb continuously. Imagine the plane was flying over land at an altitude of 1000 feet. Suddenly it flew over a barrier and gravity was 1.5x normal. In order to hold the 1000 feet altitude, the pilot would have to nose up slightly and trim for a new angle of attack, and apply more power to counteract the extra drag.
Then the plane passed over a barrier that caused it to experience .5 normal gravity. The plane would zoom up suddenly and to hold the 1000' altitude the pilot would push the nose down, and reduce power.
Now finally it flew into a zone where there was zero gravity. The plane would once again climb, unless the pilot pushed the nose down more into a zero-angle of attack. You would only need minimal engine power to keep the plane moving. But at the original normal-gravity power and main wing AOA settings you could imagine the plane would be climbing at a steady rate.
Of course if it were zero gravity, eventually the atmosphere would dissapate into space anyway, so...
