Question: what is the relationship between the buoyant force and the weight of displaced liquid?
Answer: An object will float if the buoyancy force exerted on it by the fluid balances its weight, i.e. if FB=mg F B = mg . But the Archimedes principle states that the buoyant force is the weight of the fluid displaced. So, for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.