Alfieri tells us the story of Eddie Carbone. We say he's peripheral because he rarely affects the action of the play. Eddie goes to him for help, but Alfieri can't do anything for him. When Alfieri advises Eddie to give up him his quest, Eddie ignores him. Of course, Alfieri does do one thing that causes all kinds of problems. He bails Marco and Rodolpho out of jail, which leads to Eddie's death. Overall, though, he's on the sidelines. He's not even in most scenes. He just shows up in between to comment on them.
So, how biased is Alfieri? It's hard to say. Our best guess is that he's pretty darn objective. Why do we think this? He's a lawyer. From all we can tell, he's a good one. He's honest and impartial. Throughout the play he tells people the truth whether they want to hear it or not. It's just in his nature to see all sides of things.