Now under siege from the men and elves, Thorin orders the dwarves to search for the Arkenstone, the most beautiful of the dwarves’ jewels. Rac tells Thorin that Dain is only two days away and ready to fight, but adds that the ensuing battle will be long and bloody, and that Thorin’s treasure may be the death of him. Thorin angrily refuses to listen to Rac.
Thorin refuses to listen to his people’s historical allies, the birds. This suggests that Thorin is betraying his family’s legacy with his selfish refusal to share his treasure—indeed, he’s endangering the lives of his fellow dwarves by refusing to allow them to get food from outside their home. In some sense, Thorin’s desire for his home and his treasure has made him forget, now that he has them, that a true home is founded on sharing it, on being a good host. Thorin’s willingness to fight is here presented as un-heroic.
Bilbo offers to take Bombur’s position as night watchman. While the other dwarves sleep, he puts on his armor and uses his ring to sneak out of the Lonely Mountain through the Gate. While he’s crawling through a stream on the side of the mountain, he slips, and the elves notice him. He introduces himself as Bilbo Baggins, and asks to be taken to see Bard. The elves take him to Bard’s tent, where he tells Bard that Thorin will gladly starve to death before he gives up his treasure, and that Dain is bringing an army to fight alongside Thorin. When Bard asks Bilbo whether he’s threatening him or negotiating, Bilbo offers Bard the Arkenstone as a way of bargaining with Thorin and ending the siege. Bard is surprised at the sight of a hobbit wearing armor, but recognizes the Arkenstone is of enormous value, and accepts it from Bilbo, adding that Bilbo is more worthy of his armor than many others who have worn it.
Again, Bilbo is productive while the other characters sleep. Though it seemed (and may have been true) that he originally took the Arkenstone out of personal greed and mistrust of the dwarves, it becomes clear here that whatever greed he felt is outweighed by his desire for peace, and his desire to return to his home alive. Again, it’s unclear how moral a decision this really is (in a way, it’s a selfish decision, since Bilbo is valuing his own comfort above his friends’ possessions), though it is an admirable triumph over his own personal greed. Bard and the elves show themselves to be reasonable, even likable people, because they respect Bilbo for his abilities as a burglar and a negotiator, and recognize his heroism.
Bilbo travels back to the Lonely Mountain, escorted up to the Gate by the elves. He returns to his watch and wakes Bombur up at midnight, pretending that he’s been keeping watch the entire time. He falls asleep, and dreams of food.
Bilbo does not give away the Arkenstone and then leave. He returns to the dwarves, revealing that he both feels a connection to them and that it was this connection that drove him to give up the Arkenstone: he sees his actions as something that could save the dwarves from greedily marching to their own destruction. The fact that Bilbo dreams of food harkens back to his love of domesticity, but also connects that domesticity to his heroism here: he wants to be able to return to that domesticity after his adventure, and he wants the dwarves to able to do the same.