I was wondering this myself when I watched it last night. I sat wondering, "What the crap, why?" It bothered me so much I Google'd it and found this. I honestly can't come to a real conclusion other than Harlan DeGroat (Woody Harrelson) needs to be depicted as miscreant with limited tools to navigate life. Violence is his means drugs his entertainment. If it's not clear, DeGroat is a crime boss not just a low life leader of a rural area. Killing Rodney and Harlen might simply be an example of his power over the area, he can openly kill anyone he wants and the law can do little to stop or reprimand him. Maybe the death of the two would further his image as a crime boss.
On another note I would find it understandable that he might kill someone indebted to him to send a message to others he might deal with vs collecting money he most likely will never get. So Petty's (Dafoe) death might serve that purpose and killing Rodney, I might assert DeGroat might not need a reason or that Rodney exemplified the same contempt for life and violence DeGroat had, so he offs him. When DeGroat first interacts with Rodney there's serious tension, DeGroat even goes as far as slapping Rodney, behavior reminds me of Alpha dog pack nature. Maybe DeGoat sees Rodney's lack of fear as a danger seeing there's always some weird dude following him around almost the whole movie, everyone is subject to him hence the initial drive in theater fight.
It could be one dimensional thinking of how to progress the story. For a revenge story it is slow and even timid.