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To put it as simply as possible, the wings provide an amount of lift greater than the combined weight of the aircraft and its contents. Because the shape of the wing doesn't change during flight, the amount of lift generated depends on the speed of the air going over the wing. If the wing is moving too slowly to generate enough lift to support the aircraft's weight, it falls from the sky: that's called a stall.

More specifically, the air travelling under the wing is 'compressed' and the air travelling over the wing is 'decompressed'. You know when you're in the passenger seat of a car and you put your hand out the window and the airflow makes your hand go up and down depending on the angle you're holding it at ?
Try cupping your hand a little and holding a credit card to make the palm-side (bottom) of your hand flat. The effect will be much more pronounced - that's lift.
-CB

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Q: How do airplanes stay in the sky with all the weight in them?
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