He’s bloodthirsty and ruthless, but his desire for vengeance dominates any other characteristic. Judge Turpin and The Beadle must pay for the scheme they perpetrated: stealing his wife and falsely sending him off to prison. All the other deaths are incidental, people who cross his path while he waits for his two foes to come for a shave. He’s singularly focused, to the point where he can take human life without blinking, but once his mission is complete, he’s done. He’s not a good man, but his need for justice helps us tolerate his story.
He’s an excellent barber, lol. Does that say anything about his Enneagram? We see his meticulous preparation, sharpening the razor and smoothing the lather, and then — whisk! — the close shave is done. It’s very similar to his killing spree. This is someone who likes order.
A Six? (He’s too morose to be a One.) I could consider him a Two. A gentle soul when mistreated so badly could turn to darkness. However, he takes no pleasure in his razors as objects. “At last, my arm is complete again.” They’re not a Two’s collection; the shaving tools are part of his body, part of his identity.
The ability to justify evil actions is Six-ish. Once black has been determined to be white by a Six, they can move forward with a clear conscience. When his enemies are dead, Sweeney could, in theory, revert to a normal life. The story, however, delivers its own justice. Sweeney’s moral decisions lead him to kill someone precious to him, and, after one last act of vengeance, he ends up broken by it. It falls outside of his black-and-white universe, and he can’t resolve what he’s done. When he’s killed at the end of the play, everybody’s code is satisfied, even Sweeney’s.