Buoyancy and Archimedes' principle

Buoyancy is a direct consequence of pressure increasing with depth. The bottom face of a submerged object sits deeper than the top face, so the fluid pushes up on it harder than it pushes down on the top. The difference is a net upward force, and Archimedes' insight is how clean the result is: that force equals the weight of the fluid the object pushes out of the way, regardless of what the object is made of.

That last point is why "heavy things sink" is not the rule. What matters is weight compared with the weight of the displaced fluid — equivalently, average density compared with the fluid's density. A steel bolt sinks because solid steel displaces only its own small volume of water. A steel ship floats because its hull encloses a large volume of air, so the whole vessel displaces many tonnes of water while weighing the same. Change the shape and you change the outcome without changing the material at all.

Two details are worth nailing down. Buoyancy does not cancel gravity — both act at once on a floating object, and it floats precisely because they balance. And for a fully submerged object the buoyant force does not grow with depth: pressure rises on the bottom face and the top face alike, and only their difference counts, which is fixed by the object's volume. A submarine at 200 m has the same buoyant force as at 20 m, which is why it controls its depth by changing its own weight with ballast rather than by looking for a level where buoyancy happens to match.