Two important things to remember here:

1. A wing ONLY generates lift PERPENDICULAR to the surface of the wing. If the plane is level both wings generate the same amount of vertical lift PERPENDICULAR to the ground (or gravity). IN level flight a wing with dihedral will also generate LIFT toward the center of the plane. Both wings being equally angled will deliver equal amounts of lift. Bank the plane and the "high" wing will develope LESS vertical lift and more lift toward the center. This also tends to add to the turning effect. The low wing generates slightly more lift vertically and less "inward" lift. The result is that the plane will try to return to level unless externally influenced.

2. Fully symetrical wings do not generate ANY lift at any speed unless they have a positive angle-of-attack relative to the wind. Flat bottom wings will generate lift without a positive angle-of-attack that varies with speed.