Technically, Barret isn't even a stereotype. He is what he is. Stereotyping is when you make assumptions about other people based on what someone else does.

So, if you saw a black person walking down the street and make the assumption that he must have a gun arm, then you are stereotyping based on the Barret's character. Barret is not a stereotype, however, he may fall into the stereotype that you already have in your head about what a black person is or how they act.

Oh and by the way. If you looked at Barret's character and said "Oh he's a stereotypically black man", that my friends, is being racist.