Firepower is what makes or breaks a pirate. By the time of the Mary Rose, canons were a common sight on ships. In my studies, I have found what they used before this form of heavy artillery. Illuminations show archers on ships shooting at another ship. Other images show staff slings holding a corked bottles of lime that are about to be flung. Lime was used as an early chemical weapon, designed to blind opponents. Spears, pikes, and grappling hooks were also used. The first use of a major weapon, a catapult, was by pirate John Cabbie. Swords and daggers have to be shorter than those used on land because of the close quarters on a ship. Handguns like blunderbusses and harquebusiers were in use at the end of the period.
Next time, Booty on A Pirate's Life!
(From my SCA class, So You Want to be a Pirate)