Bilbo was witness to the attack, and he managed to stand up on the tree. While completely unlike him, he felt a fire within his heart, one of courage. Thorin needed help, and he may have been the only one there light enough to leave the tree without disturbing it.

At the same moment, The White Warg clamped its jaws around Thorin. Kili's eyes widened in horror as Thorin yelled out in pain; the sound was foreign to him, for he'd always believed his uncle immortal. For a young dwarf like Kili, nothing had ever seemed strong enough to harm Thorin, and yet here he was, at risk of being slaughtered before their eyes.
Dwalin tried to leave his place in order to assist Thorin, but the tree branches he held onto broke, swinging him over the edge and preventing him from reaching his king.

Thorin managed to hit the warg's head with the pommel of his sword, a hit enough to make the beast roar and throw him several feet away. Thorin landed heavily, his sword far from reach, his vision going dark. As it was, he was moments from losing consciousness, and Azog knew that.
The Pale Orc smirked cruelly, his eyes locked to Saeril. "Bring me the Dwarf’s head," he commanded the orc nearest to him. "This one is mine." With that, he gave a roar and charged towards her, his mace in hand.