You need to understand an aeroplane operates in a force field so is not like a spacecraft. A spacecraft will accelerate if a net force is applied, otherwise it will continue in a straight line.
An aeroplane behaves similarly in the two dimensions parallel to the Earth's surface but not when altitude is concerned. Here the force field generated by gravity comes into play. As you climb, you move through this field. Although you gain no momentum at a steady rate of climb, you do gain potential energy by changing your position in the gravity field. This requires an input of work/energy. And that comes from a vertical vector greater than the weight of the aircraft.
Newton's 3rd Law only really brings anything to the party when you try to explain how propellors and turbines work. People don't normally explain lift this way because a wing is completely different to a thing which merely deflects air downwards.