The Maturation of Bilbo Baggins
As the group enters the forest, Bilbo ends up taking the role of leader more often. This leads him into growing up or maturing faster. When Bilbo has come face to face with the spider he ends up killing it. Then he frees his friends when they also get trapped and tied up by the spider. In this chapter Bilbo proves himself as brave and daring. Without Bilbo the dwarves would have surely died in the forest.
"Somehow the killing of a giant spider, all alone by himself in the dark without the help of a wizard or the dwarves or anyone else, made a great difference to Mr. Baggins. He felt a different person, and much fiercer and bolder in spite of an empty stomach as he wiped his sword on the grass" Chapter 8, pg. 155
Also in the spider scene in chapter eight, this is where Bilbo names his sword, Sting. This signifies he is getting more comfortable with himself as he is maturing throughout the novel.
When they get to the mountain and have to go confront Smaug the dwarves naturally turn to Bilbo, although at first they could not open the door to the mountain. This made the dwarves very frustrated and they tended to get extremely annoyed with Bilbo. Finally the door was open with Bilbo's ability to remember Elrond's advice. Once again the