Remember that when forces are balanced, no acceleration will occur. But a constant velocity may. So, in wings level flight, if L=W there is [B]nothing[/B to say that a constant rate of climb or descent will not result! In S&L flight, constant tiny corrections of attitude are made to maintain level flight; this changes L so that a correcting force is applied in the appropriate sense; that is then changed when the desired level is regained.
In the extreme case of an aircrfat in the hover (let's say a Harrier for simplicity), all the aircraft's weight is opposed by the engine thrust. To descend, thrust is reduced which causes a downward acceleration; if thrust is then restored to the same value as weight, all that will happen is that the aircraft will continue to descend at the vertical velocity it had at that particular moment!