stranger12,
I was going to post much along the same lines as most of the other responses here, particularly when I saw the diagram posted by ArcticChiller.
My physics teacher, Doc Strawbridge, would be turning in his grave - "Class, there is no such thing as centrifugal force!"
If you mentally modify ArcticChiller's picture by removing the Centrifugal Force vector and the Resultant Load vector, then you have the actual forces acting on an aircraft in a turn. As mentioned above, the Lift vector has to be larger, so that the Vertical component still equals the Weight and the Horizontal component provides the force necessary to turn the aircraft. In order to increase the Lift, you have to increase the angle of attack, by pulling back on the stick.
The aircraft in the picture could not turn if the forces were as shown, because they are in equilibrium.