Assume that an airplane is flying level. If I understood correctly in this situations there are four forces acting on it: weight, thrust, drag and lift.
Lift depends on air density, airspeed, wing area and lift coefficient. In the situation described above all of these parameters are constant with the exception of airspeed which can be changed by pilot. So when increasing airspeed lift increases too which makes sense because that seems to be how planes take off.
However when you watch footage of airplanes accelerating (for instance when a fighter turns the afterburners on) they seem to be able maintain altitude.
At this point I see three possibilities:
- The airplane doesn't climb or climbs very little because the pilot simultaneously compensates.
- I have the wrong impression and the airplane does climb.
- My reasoning above was wrong and there's actually no reason for the airplane to climb further.
So which one is it?