Out of all characters in the movie, I hated this punk the most. First, he is with English Bob and when English Bob is sent away, he hangs out with Little Bill. Once Little Bill is is killed, he moves on to William Munny. All this little rat cared about was getting information on the fastest gunslinger in the west.
I think that was the point. The whole time, Beauchamp is trying to romanticize "The Wild West," but in reality they're all just vicious killers and bullies. Like the people of the day (and us even), he was licking his chops to hear stories of folk heroes rescuing women from bandits and gun fighting in the streets.
But he finds out his "righteous" white savior is nothing more than a drunken coward who can only shoot unarmed Chinese laborers, the noble sheriff is a self-righteous bully with a bad temper, and the legendary hero is nothing more than a lucky killer. Every character is a deconstruction of the genre, and I think Beauchamp is an excellent representation of the audience.