How does annabeth change her opinion of percy as they traveling during the quest

She starts to respect him as she sees his skills an courage.

"Living to ideal ends without any mixture of self-indulgence lowers the value of benevolent and thoughtful men we know" 
"Refusing luxuries, simply as unfit for his habit; quiet and gentle as a child in the house"
-These lines are an attempt by Emerson to portray Brown as an everyman, that slaves can associate to. Brown has been exposed to the perils that slaves are subjected to when he saw their harsh realities as a child. This positions Brown as a relatable fellow amidst of being convicted for the violence behind his anti-slavery movement.
Emerson is a supporter of non-violence and is a surprising supporter of Brown. There is an aspect of Brown that he tries to bring to the surface. Emerson wants Brown's good intentions and motives so as to remove the spotlight on the main point of the movement.