You've ignored an important element of flight and that is lift. The below graphic explains the basic principles of flight.
For the sake of simplicity lets assume straight level flight. Four forces act upon an aircraft in flight, thrust is balanced by drag and weight by lift produced by the wing. The aircraft will move in the direction of greater imbalance. If weight is greater than the lift produced by the wings the aircraft will descend, if drag is greater than thrust the aircraft will not move forward as a consequence the wing will cease to provide lift and the aircraft will descend.
In the vertical (the aircraft is climbing vertically) the aircraft becomes a rocket the wing does not produce lift, so both the weight and drag must be overcome by engine thrust. Here thrust to weight ratio > 1 will allow the engine to propel the aircraft by overcoming the force of gravity and drag.