Remember Lift is less than weight in a climb.
So what did I miss in my studies? Suppose you're in steady level flight and accelerate whilst maintaining the same angle of attack. Doesn't the increased speed result in increased lift over and above the weight? And, if so, doesn't the aircraft climb, albeit slowly?
And can't you convert a power off descent to a momentary power off climb? No thrust component to add to the vector so it is all lift which is greater than weight in this case.
Just asking.