The question "Why no weapons aboard ship?" isn't on topic in my opinion, and this is backed up by the question's opening line:
While my question regards piracy in general, the movie Captain Phillips is what brought it on due to it being a true story.
The question itself is obviously not about the movie, but about the events depicted in the movie:
why in hell if you are going to drive a ship full of cargo worth millions, through pirate waters, you wouldn't have weapons?
I'm tempted to flag it for closure for being off-topic, but none of the available reasons seem applicable.