Rope

Since Eddie appears to be quite the cowboy, and he's super controlling (like, so much so that he tries to bend reality to what he wants it to be), it seems appropriate that he ends up showing off his lassoing skills. He says he needs to practice—which isn't too surprising, given that he's a rodeo cowboy:

"Little practice. Gotta' stay in practice these days. There's kids out there ropin' calves in six seconds dead. Can you believe that? Six and no change. Flyin' off the saddle on the right hand side like a bunch of Spider Monkeys, I'm tellin' ya', they got it down to a science." (218)

So, he just hangs out in May's room roping bedposts while he and May chat. This is a not-so-subtle bit of sexual innuendo (he picks bedposts for a reason): he's basically showing off some Christian Grey-style skillz. He's also, a little menacingly, referencing the fact that he's pretty much "tied" May to him—her sexual attraction to him is as tight as a lasso.

Seems harmless enough, we suppose, but when the conversation turns to May's boyfriend, Eddie's "practice" turns into a kind of nasty demonstration of his intent/ability to control the situation.

When May asks what Eddie intends to do when Martin shows up (since Eddie is so eager to meet him), Eddie claims, "I'm gonna' nail his ass to the floor. Directly" (243). To add emphasis to that threat, he then ropes the chair right next to May and yanks it "violently" toward him.

The message there seems pretty clear—Eddie's got his lasso or "noose" around this whole situation, and he intends to make sure everything goes down his way. He's going to make sure Martin knows who's boss. So, the rope seems like a pretty clear symbol of Eddie's controlling tendencies.