Afrequently quoted rule of thumb in aircraft design is that wings should produce about 1000 n of lift per square meter of wing. (the fact that a wing has a top and bottom surface does not double its area.)

Correct. The lift is directly related to the area of the wing.

Explanation:

The bigger the area of the wing, the bigger the lift will be. But there is a catch: the drag will also be bigger. The denser the air is, more lift and more drag you'll find. At low altitudes, air has more pressure. The higher the pressure is, more lift and drag you'll find. Cold air has more pressure than hot air. Therefore, it's easier for an airplane to takeoff at low altitudes and cold air. But given that drag is also bigger at low altitudes, airplanes tend to have their flight cruises at higher altitudes where there is less lift but there is also less drag as less drag is desirable for saving fuel and flying faster.