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Probably limited a small bit by structural strength, i.e. more acceleration means a stronger and heavier structure. For manned rockets, the G forces are even lower to accomodate the astronauts. So I'm assuming that even lower accelerations are only possible if you trade off fuel efficiency.
This aircraft is used to train astronauts in zero-g maneuvers, giving them about 25 seconds of weightlessness out of 65 seconds of flight in each parabola. During such training the airplane typically flies about 40â60 parabolic maneuvers.