Why does a raw egg have more inertia than a boiled egg?

There isn't any reason why it should, since nothing has entered or exited the egg during the boiling process. The thin paper membrane just inside the shell of an egg is impervious to just about everything including bacteria, and the egg shell itself is nearly equally so. Therefore, the egg should contain the same mass, at the same volume (and therefore the same density) before and after boiling. It does nothing more than to congeal a liquid mass into a solid mass, but does not gain mass. It has also retained it shape and therefore has not incurred a change in aerodynamic, or hydrodynamic properties that might slow or speed its descent.