Merle desires to turn Michonne in so that he may be absolved from his sins. Not that he completely cared what everybody in the prison thought of him; but he cared about his brother and his relationship with him. He saw how much the people in the prison meant to Daryl and he wanted to make things right for him. Listen to what he says:
Merle: "I want to be with my brother. My brother, he wants to be in the prison. This little trip, maybe, it will keep that place standing. If I put it off, maybe all is forgiven.........You gotta play the hand your dealt........I only got one."
Michonne notices the weight Merle is carrying around and says:
Michonne: "You talk about the weight of what you have to do, how you can handle it. A bad man, someone truly evil, their light as a feather. You don't feel a thing."
This is probably the nicest thing Michonne has ever said to Merle. She is telling him that there is hope for him and that he can change things. Once Michonne notices that talking Merle out of this trip by telling Merle how not so bad he is.......that its not going to work because Merle doesn't think much of Merle, but his brother? Well that is a different story. He picked a side, and that side was his brother and everything he did thereafter was to fix that.