The reason pirates say "arr" is because Robert Newton, who played Long John Silver in 1950s Treasure Island and then in several movies after, had a very thick West Country accent which he further exaggerated in his film roles. He also played Blackbeard in many movies, often available on YouTube, and speaking personally they are all a blast as long as you can get past the parts where Robert Newton isn't on screen. Many later pirates roles such as Geoffrey Rush in Pirates of the Caribbean were basically doing Robert Newton impressions (the other ones are impersonating Errol Flynn).

Now that said, it is true that quite a few famous pirates, including Blackbeard himself, were from the West Country given that pirates were overwhelmingly former sailors in the navy or on merchant vessels, and Bristol was a major port (Marcus Reddiker's Villains of All Nations goes into great detail on the origins of pirates and pirate crews). So if you want to imagine Blackbeard did actually sound like this you can.

Unfortunately something I have not been able to find out is whether Newton's decision to use a West Country accent was actually based on these historical considerations. He was an accomplished actor, and his accents ranged from RP when he played Horatio in Olivier's Hamlet to a Dickensian Cockney as Bill Sikes in David Lean's Oliver Twist, so it was clearly deliberate, and could plausibly be based on history, the fact that filming was primarily around Devon and Bristol, or because it was a convenient way to portray an old timey lower class.

EDIT: Took me a second to dig up, here is a good discussion of the various bits of pirate terminology that are in pop culture and how close they match actual nautical terminology from the time.