What do you call someone who steals from and lies to the people he's supposed to govern and protect? We can think of a few naughty words, but "antagonist" seems like a good fit, too. He also tries to block and even harm our protagonists at every turn. We get an early whiff of this when Doon confronts him on Assignment Day, and the mayor is quietly menacing. But by the time the mayor is about to have Lina thrown in prison, he's moved to actively messing with them and trying to hurt them. So the mayor isn't just being a jerk-face to the whole city, he's opposing the protagonists, too, which makes him Public Enemy Number One.
Looper is pretty shifty, which makes him a good candidate for someone we don't like, but not necessarily antagonist. What does put him in that category is his being selfish enough to actively contribute to the decline of his community. He parcels out stolen and hidden goods to the people he likes, or the people who can pay his high prices. Because, you know, it's best to live it up while you can rather than try to find a solution that would help everyone.
He's not super-active against our protagonists, but we're pretty sure that if Looper had caught Lina or Doon spying on him, he would've taken steps to silence them. And sleeping with the fishes might've been one of those steps, just sayin'.