A boat floating in water, or a hot air balloon suspended in the air are examples of buoyancy. It was Archimedes who discovered the law of buoyancy, namely that a body immersed or suspended in a liquid or gas is buoyed up by a force equal to the weight of the liquid or gas displaced by the object.
In the case of a boat, the force of buoyancy is equal to the weight of water displaced by the boat. As the boat enters the water it will sink into the water until enough water is displaced to equal the weight of the boat and its contents. Thus, as weight is added to a given boat, the water line will rise.
A hot air balloon rises because hot air is less dense than cold air. This is because the molecules of air are driven farther apart from one another as the temperature increases. The air becomes less dense.
The balloon displaces its entire volume. So the volume of the balloon is equal to the volume of the air it displaces. By Archimedes Law, the balloon is buoyed up by a force equal to the weight of the displaced (cold) air, which is greater than the weight of an equal volume of the lighter hot air contained in the balloon. Hence, the balloon rises.