How many times have you read New Moon (NM)? Most people need to read NM more than once to get the full Jacob experience. The first time through many people are so traumatized by Edward's leaving that they read the chapters while he is gone in a Zombie like state and never get the chance to fall in love with Jacob the way Bella did. You only really see Jacob's true personality in NM. After that, he is under too much stress to be himself. One of the most appealing things about Jacob is his contagious happiness. We see that in NM, but it is replaced by profound sadness until he imprints upon Renesmee.
Jacob truly loves Bella more than anyone he has ever met until he imprints upon Renesmee. Bella truly loves Jacob, but never as much as she loves Edward. It is almost as if she imprinted upon Edward. Jacob and Bella's relationship is doomed from the start. Bella see this, but Jacob cannot. One of Jacob's most endearing qualities is his eternal optimism. It is also his fatal flaw. He knows that Bella is devastated by Edward's leaving, but he is certain that given enough time, he can help her to a full recovery. He never knew that the recovery that he was witnessing in NM was more attributable to her growing awareness that Edward truly loved her than her growing love for him. In NM he displays a great deal of compassion and patients for Bella. He knows that it is going to take a lot of love and time for her to get over Edward, and he is willing to give her that time and that love.
Bella and Jacob share love languages. Both of them express and receive love through physical touch. Look at how natural it is for them to hold hands. Consider how easily they hug each other. This isn't sexual; even though, Jacob cannot help but have "impure" thoughts about her, this is love. Both of them express and receive love through acts of service. Look at how Bella "takes care" of everyone she loves. Consider how Jacob will do whatever it takes to make Bella happy. In NM we see them "clicking" very naturally. If she hadn't been irrevocably in love with Edward, it might have worked. (I am also sure that, without Edward, they would have never found each other.)
Then Bella finds Alice in her house and everything changes. Jacob just ran out of time. And I mean just ran out of time. If he had kissed Bella before Edward's phone call, everything would have been different. Bella had "imprinted" upon Edward, but she sticks by her decisions. If she had decided to give her love to Jacob, that would have changed everything. Some part of Jacob knows how close he was, and it frustrates him to the very core of his being.
Jacob's behavior after that would have been unforgivable if Edward were just another boy. If Bella had been in love with Mike Newton, Jacob would have probably bowed out with good grace. However, Edward is not just another boy. As far as Jacob knows, Edward is a blood sucking leach. He is a cold one. He is a soulless undead vampire. He is a mortal enemy of the Quileutes. And most of all Bella's choice to be with Edward must eventually lead to her death. Bella choosing Edward over him is like suicide, and that is SO NOT OK! If the person you loved was making a decision that you knew was going to kill them, wouldn't you do whatever was in your power to stop that? And that is exactly what Jacob sets out to do. The consequences of failure are so unacceptable that he willing to take any risk to prevent Bella's death.
There is another reason that is very strong but not as strong. It takes Jacob a very long time to forgive Edward for what he did to Bella. By leaving her, Edward killed Bella in a very real way. Instead of becoming a vampire, when Edward left, she became a zombie. He ripped out her insides and left a huge gapping hole. When he left, it was almost as if he had taken her heart. He can't trust Edward to never do that again. He knew that he could help her heal from a broken heart, but if he really did turn her into a vampire and took her soul, he knew he could never heal that.
It was necessary for Jacob to make Edward face what he had done to Bella as only he could. I really wish that Charlie could have given it to Edward with both barrels and let Edward see the consequences of his actions as only Charlie knew them, but Edward can't really read Charlie. I believe that if Edward could have truly read Charlie, it would not have been possible for them to be in the same house much less same room. Jacob needed to know that realization of Bella's pain was torture to Edward. We all needed to know that it would easier for Edward to endure Jane's tallent than be confronted with what he had done to Bella. I suspect that if Jacob could have dumped Bella is full zombie mode on Edward; he would have been on his knees. This is critical because Jacob, and the rest of us, needed to know Edward's remorse. Remorse must come before repentance for that repentance to be real and lasting.
I fully agree that Jacob was a really jerk in Eclipse (EC). Bella knows that Jacob is a jerk. He is under way too much stress to be himself. He is trying anything and everything he can think of fighting with all of power to win her away from Edward, but he is too young to know the best ways to fight, and the cause is too lost. This bothers Bella, but she puts up with his crap because she knows that under all the pain and desperation is her Jacob. If you didn't fall in love Jacob in NM, you won't be able to see this.
The other thing that you have to understand about Jacob is that he is not doing this for himself. He is doing this to save Bella's life. At first he doesn't trust Edward not to kill her. Then he discovers that she fully intends to become a vampire, and he goes into over drive. Eventually he comes to really understand that she does love Edward. Eventually he becomes reconciled to her desire to become a vampire. He even comes to wedding to wish her well and say goodbye. He only looses it when he understands that Bella is contemplating suicide yet again with her desire for a real honeymoon. Jacob's ability to reconcile himself to Bella's decision demonstrates the goodness of character more than anything else could. And it wasn't just imprinting upon Renesmee either. The sound of her heart beat assuring him that she was still "alive" would have been enough. Even when the center of his universe was changing, he still heard that sound.
After that he was able to be the friend that Bella wanted and needed. Renesmee was a big part of that, but not the only part. He knew that Bella was going to be OK. She wasn't some soulless undead thing, she was still Bella. She was herself, and she was happy. He could live with that. Even if he hadn't imprinted upon Renesmee, he could have bowed out with grace. He probably wouldn't have been able to hang around anywhere near as much, but he wouldn't have been in the kind of pain that tore Bella apart. This is because his desperate measures were never for him, but they were always for Bella.
One of Jacob's most endearing qualities is his selflessness.
In spite of all of his inner turmoil, in EC when Jacob discovers that the Bella is facing a danger that has the Cullen's over their head, he says without a second thought, "No, you will not be alone." He doesn't even like the Cullens yet, but he is willing to stand beside them against an overwhelming force to protect Bella.
When Leah, through her own pride, places herself in danger, Jacob with no thought to he own safety leaps into action to protect her. He doesn't even like Leah, but he willing to sacrifice himself to save her.
After he knows that his battle for Bella is over and he has lost because she is married to Edward and carrying his child when he learns that his brothers intend to kill her, he leaves everything that he has behind him, and runs to protect her.
While she is dying carrying Edward's child, he still can't help but be there for her; even though, it is agony for him to watch her die.
When Bella and Renesmee face certain death at the hands of Volturi, he is still willing to sacrifice his life in a vain attempt to protect them. We know that Bella intended for him to run away with Renesmee, but he didn't. We know everything turns out alright, but he didn't.
Who doesn't love Seth? Jacob and Seth share the same basic qualities. The difference is that after fighting alongside Edward, Seth couldn't see him as a vampire in the soulless undead creature sort of way. Because of this, Seth never shared the despair that filled Jacob. In so many ways, Seth really is a little Jacob.
That is why we love Jacob Black.