Archimedes’ principle is as follows: The buoyant force on an object equals the weight of the fluid it displaces.
A really large, light object is probably going to float. This is because a large object will displace a lot of water, creating a big buoyant force. And a light object will have a small force of gravity. With a small force of gravity and a big buoyant force, the object will definitely float.
But a really small, heavy object is probably going to sink. This is because a small object will not displace much water and will have a much smaller buoyant force. And, being heavy, it will also have a large force of gravity.