Teardrop is the fearsome bad guy you want to like. He is the meth addict, meth "cooker", intimidating to everyone in the story from the other meth cookers to the police to Ree and her siblings. No one wants to make Teardrop mad, as the author suggests bad things happen. We see him make a few threats, and there's questions about whether or not he abused Ree when she was young.
But for all of these flaws, Teardrop still cares for his girlfriend and for Ree, and, you can tell, for Ree's father, certainly dead out there somewhere. He comes to Ree's rescue near the end, when she might be killed herself, and thereby redeems himself in a way with her and the readers.