A hot air balloon climbs because warmer air inside the envelope becomes less dense than the surrounding atmosphere, and buoyant force quietly does the rest. The balloon displaces a large volume of outside air; by Archimedes principle, the upward force equals the weight of that displaced air. If that upward force exceeds the combined weight of the fabric, basket, fuel and passengers, the whole system rises without any wings or engines.
The physics turns on controlling gas density with a small temperature difference. Heating the enclosed air raises the average molecular kinetic energy, increasing pressure at constant volume, then allowing some air to vent so the pressure inside roughly matches the outside while density drops. This lower density gas creates a net upward force that can support tons, because the displaced cold air over such a large volume weighs even more. The energy input is modest compared with the weight lifted because the atmosphere itself supplies the support; the burner only adjusts the density contrast.
At altitude, pilots fine tune lift by pulsing the burner to manage internal temperature and by exploiting ambient pressure gradients. Convection inside the envelope helps keep the hottest air near the top, where lift is most effective, while the open bottom allows cooler air to enter if the flame is reduced, increasing density and bringing the balloon down.
