I think that the theory works very well! If it didn’t then we wouldn’t be able to have huuuuge ships like Ferrys floating on top of the sea. If those forces were slightly out of balance, those ships would sink so that means the theory must work very well 🙂
It was Archimedes who realised that all bodies that are lighter than water displace their own weight (more correctly mass to you and me the two things are pretty much the same) of water. It happened when he made his bath overflow and the story goes that he was so excited he ran out into street, dripping and naked, shouting “Eureka!!!” (Greek for “I have found it”). It was the original “Euraka moment” that scientists sometimes refer to when they have an idea. Fortunately we tend not to go running about the streets naked when we do make a discovery…….
Ships float because, depsite the fact they are made of iron, which is much denser than water and simply sinks, they contain vast quantities of empty space containing air so their AVERAGE density much less than that of the surrounding water.