Stalling speed increases in a turn because of the increase in load factor. The airplane isn’t actually heavier. It is fake weight, but the airplane reacts to it. With more weight, fake or not, the angle of attack needs to be increased to maintain lift. Even in level flight a heavier identical airplane flying at the same speed (with increased power) will need to fly at a greater angle of attack to maintain altitude. The greater the angle of attack the closer your are to the critical angle of attack, or stalling speed. A wing on most general aviation airplanes stalls between 16° and 18°. An identical heavier airplane, loaded with fake weight or actual weight, will reach the critical angle of attack at a greater airspeed, thus entering a stall.
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