How we cite our quotes:
[Jacob:] "She's not dead," [Edward] growled. "She's going to be fine." I wasn't sure he was talking to me anymore. Turning away, leaving him with his dead, I walked slowly to the door. (18.93)
After Edward injects Bella with his venom and her heart stops, Jacob believes that she'd dead. He gives up fighting for her life before Edward does. Do you think that part of him is relieved that at least she's not going to be a vampire?
[Edward to Bella:] "It goes against the grain… letting you wrestle with lions. I was having anxiety attack the whole time." (21.147)
Although Bella is a vampire now, strong enough to wrestle with lions, Edward has trouble not thinking of her as the clumsy, fragile girl she used to be.
[Jacob to Bella:] Maybe it's not the look as much as… you are Bella. (22.64)
Jacob realizes that although Bella looks different, her personality and essence have remained the same.