Floating ships made out of iron...

Which magnitudes change if the ship is loaded up?

The picture above shows an empty ship. The buoyant force equals the gravitational force.
If the ship is loaded up, its mass changes and therefore its gravitational force as well (see picture below).

The ship sinks deeper and displaces more water.
Due to this, the buoyant force, which is directed in the opposite direction, increases.
Buoyant force and gravitational force are equal again.