I root against Lebron every time he plays the Celtics. Other than that I've tended to root for him a part from 2011, 2013, and 2014 Finals. But even then that had more to do with my hatred for Dwayne Wade and Pat Riley.
I remember wanting Lebron to be the next great player like he was projected to be. There was a line of so many high school to pro disappointments and he was supposed to be the sure thing. I wanted to see that next great player. He has been that great player, which is part of was is so astonishing about his career. His hype was so great and he's managed to live up to it.
Sure, he can be obnoxious sometimes, as will anyone who is so heavily exposed culturally. But there are players still more obnoxious among his contemporaries (Chris Paul, Blake Griffin come to mind).