Is there a sense of justice in Dr Jekyll and Mr Hyde and which parts of the novel shows justice or injustice?

Toward the end of the third chapter, "Dr. Jekyll Was Quite at Ease," Jekyll is speaking with his lawyer, Mr. Utterson, about his will.  Utterson has confronted Jekyll about the will, which concerns him, because, in it, Jekyll has left all his worldly possessions, should he disappear for a minimum of three months, to Mr. Hyde (a man who is completely abhorrent to Utterson in every possible way).  Utterson claims that he will abide by Jekyll's wishes but that he can never like Hyde, to which Jekyll responds, "'I don't ask that [...].  I only ask for justice; I only ask you to help him for my sake, when I am no longer here.'"  Therefore, it seems that, for Dr. Jekyll, it is just that this terrible little man who we learn later is a murderer, essentially comprised of nothing but the very worst parts of the relatively good doctor, should benefit from Jekyll's demise, should it come.  Most would argue that this seems relatively unjust, that Hyde should never benefit from someone else's misfortune, let alone the misfortune of the man whose own downfall permits Hyde to live.
Justice never really seems to be served in this novel.  Jekyll should not have attempted to rid himself of his "evil qualities" because the mixture of both good and bad is something that each person needs to work out for him or herself (as Stevenson seems to be suggesting).  Jekyll admits to experiencing a "profound duplicity" that resulted in a "morbid sense of shame," in his final letter, but it is not just for him to attempt to rid himself of part of what makes him human so that he can have an easier time of it. One could argue, on the other hand, that it is not just for Jekyll's strict, Victorian society to install such rigid rules regarding conduct that a mostly good man feels the need to go to such lengths to shed any semblance of moral ambiguity he possesses.  Further, justice is never really served to Hyde for the wrongdoings that he commits; he does take his own life, but that is his choice, and the capability to choose to avoid punishment by disappearing into Jekyll and, later, death, seems unjust as well.