"Greatest" Weapon really depends on your definition of power. Lethality-wise it would be bio-engineered weapons, since a vaccince resistant smallpox strain would be able to kill billions, but that ought to be too grim for this lighthearted series. If we go by explosive force it would be the the Tzar Bomb, but you could argue for nuclear bombs in genereal or even something like the Neutron bomb. Even something abstract as rhetorics could be named, since it is able to give birth to and bring down entire nations, start wars and even rationalize historical atrocities. Money would also be an option, but those more abstract entities are not science-related enough, I think.
Personally, I'm with the people that name things like radio communication or flight related stuff, like some sort of ancient aeroplane or hot air balloon. Maybe even both, who knows, glasses wearing, katana swinging and walkie talkie using stone age warriors in an ancient hot air ballon would really fit the series :)