"Leaving the weapon behind?" he confirms, trying to build a clear picture, "do you have an idea of what time this was? How long before the weapon was used?"

Perhaps, if he can pin down the exact window they can try and map where everyone was on the ship at that time. There are a lot of people, though, and a lot of places for people to hide. That, and he doesn't know all of them well enough to tell when they're lying. For all he knows, Edgeworth himself might be lying.