The reason why balloons take off:

That is correct!
To make the balloon rise, the balloon pilot has got two possibilities:

Drop some ballast to make the balloon lighter or

heat the air in the balloon envelope even more to increase the buoyancy.

If the balloon pilot wants to sink, he must get rid of the hot air. Thus the balloon has got a small opening through which the warm air can escape. Then the balloon is affected by less buoyancy and sinks downwardly.