Exercise apparatus and method with selectively variable stabilization enabling a user to progressively increase his/her core body muscular strength. In various embodiments, the exercise apparatus includes a resistance cabling system providing a user defined line of motion, and a partial stabilizer pad being adjustably positionable offset from the line of motion, wherein the user's core body is positionable against the pad and required to resist the torque created by the offset. The user can progressively increase the distance between the line of motion and partial stabilizer pad, in order to progressively increase the force which the user's core body must resist to maintain an upright stature. In this way, the user can progressively, over time, increase his or her core body strength. A vertically and rotatably adjustable handle/arm assembly, resistance cabling and pulley assembly, and an overall exercise apparatus having a relatively small footprint but allowing multiple variable exercise routines, are also provided.