The narrator repeats that Claggart was very handsome except for his chin. Billy, though, was much more good looking. The narrator guesses that this may be the reason for Claggart's malice toward Billy. His comment about Billy's handsomeness in the mess hall may have revealed that Claggart was secretly jealous of Billy's better looks. He backs up his theory by noting that envy often leads to hatred.
Claggart's protruding chin may hint that, just as something is out of place in his otherwise attractive appearance, something is not right in his supposedly moral nature. The narrator's focus on physical appearance extends to the idea that perhaps Claggart too is focused on such appearance, and jealous about it.
Claggart's envy was deeper than mere jealousy of good looks, though. According to the narrator, he was envious of Billy's upstanding moral character and innocence. The narrator says that Claggart could hide the evil within him but could not get rid of it. Claggart's awareness of his own inability to be as noble as Billy intensified his antipathy toward Billy.
In the narrator's view, Claggart is envious both of Billy's beauty and the good character it signifies. The description of Claggart becoming even more evil because of his awareness of his inability to get rid of that evil—in other words, Claggart wishes he could be good but his nature doesn't allow him to be, and so in jealous anger he becomes even worse. As an aside, such a psychological dynamic corresponds to descriptions of the characters of those who have been damned, such as, say, Mephistopheles in the play Dr. Faustus, who out of despair for his own inescapable damnation seeks to lure others to hell.