Several years ago I was a passenger on a near cross-country flight when the pilot came on the PA and announced that we were climbing towards our cruise altitude, on autopilot, and as our fuel load was burning off, and the plane's weight lessened, we would be climbing about another five thousand feet from our cruise altitude.
I wondered why the autopilot, instead, would not make micro-adjustments to the angle of attack to maintain the same altitude, rather than waste fuel making an unnecessary climb.
I realize that maintaining the same exact altitude is probably not realistic, but autopilot, I would think, ought to be able to maintain cruise altitude within about one thousand feet.
This was on a Southwest flight, so it had to be a Boeing 737.