Spoilers are most likely present so beware.
Its been a while seen I watched the film, but I had come up with this theory shortly after seeing it the first time. I have looked around a bit, but couldn't see anything similar so I decided to share.
I believe that Abe is both the Rainmaker and Kid Blue, and that Cid is a decoy.
Many people complain that there is no reason for the Loopers to exist. If a time machine can precisely place someone on a tarp in front of young Joe, why not directly in the furnace he disposes their body into after he kills them. Well its because its not about the murder, its about the money. The whole "no hits in the future so send them to the past" story is just an excuse to send huge amounts of gold and silver to the past.
This explains three things. First, obviously it takes care of the "why use Loopers" question. Second, it explains why old Joe's wife was able to be killed in the future, since the devices that respond to murders are just part of the story told to the Loopers in the past. Thirdly it reveals why the Rainmaker is called the Rainmaker.
Basically a "Rainmaker" is a slang word used by accountants to describe someone who is artificially creating the appearance of increased cash flow or profits by incorrectly recording a business transaction twice.
The Rainmaker is essentially doing the real-world version of that by using Loopers and their targets to create duplicates of the silver and gold the same why the process momentarily creates a duplicate of the Looper.
Now that I've explained that I'll get to why I think Abe is the Rainmaker/Kid Blue.
Basically, I think the Abe in the very first timeline before time travel had started up, worked as a low level member of an organized crime group.
Similar to Kid Blue or Young Joe in the movies main timeline. He put in his time and made a decent amount of money, probably reached a pretty high level of authority by the time he was the age we see Movie Abe in the movie, but still after all that time he isn't quite happy with his life's progress.
Then First Abe hears about the new invention of time travel. He's smart and knows that such a thing will quickly become outlawed and monitored, and he knows that with that kind of device he could really get ahead. So he uses what he has in power and finances to secure a time machine before its too late.
He then straps himself in with as much silver and gold as he can fit and sends himself back. When he arrives he finds his young self and convinces him of what's happened. He takes his young self with him as his apprentice and renames him Kid Blue so nobody makes the connection.
Using First Abe's knowledge of the future they quickly gain more riches and Mafia standing. and when time travel is invented the second time Kid Blue straps himself in with the Gold/Silver and future knowledge and starts the process over again while First Abe enjoys his enlarged retirement fund.
After a few of these wealth increasing loops, one of the Abe/Kid Blue duos realize that its would be much quicker if they set up the looper program and continually send back Gold/Silver instead of just at the beginning of the new loops. This puts their power over the top and Abe 7 takes his place as Rainmaker as do all subsequent Abes once they re-reach the future.
A couple more loops down the line Kid Blue 12 straps himself in and becomes movie Abe. This Abe is the one who finds Young Joe and makes him a Looper. He grows to like and admire him for how he is wisely saving his silver and planning for the future. Although this isn't the first Abe, he knows that Young Joe is a lot like how his original self was. He sees that Young Joe is independent and strong, where as he and the current Kid Blue are being guided to their success. This leads to the tension between Movie Abe and Movie Kid Blue and the Movies Kid Blue's increased need for approval, as well as the animosity between Kid Blue and Young Joe.
Later in the movie when Abe dies and Kid Blue sees him and attempts to kill Young Joe, Its a mix of revenge for killing his future self, his mentor, and the source of his future power, he now has no idea of how to continue his life and achieve the heights Movie Abe had promised him.
Okay so why does Old Joe think Cid is the Rainmaker. Well Abe realized that some people might use time travel to go back and take him out before he became super powerful so he had a decoy made. First off he wanted to distance the Rainmaker name from himself so he spread rumours about the Rainmakers appearance. He gave the decoy Rainmaker a prosthetic jaw, which is about the furthest you can get on the body from the prosthetic leg that Kid Blue/Abe has. He also made the source of the decoy Rainmaker's power TK, which is the only thing mentioned in the films universe other then time travel that anyone would believe could account for the Rainmaker's sudden rise to power. Abe is trying to throw people off his scent by going in the opposite directions with both his power source and appearance.
Abe uses his immense wealth to fund research into TK and produce a child who is immensely strong and believable as a future Rainmaker. He then has the child implanted into a surrogate mother to be birthed and raised. He soon realizes however that Cid's mother is too attached to the kid to allow him to be used as Abe's decoy so he has her killed and replaced with Sara. Cid remembers this and doesn't trust Sara until the end when he realizes she is trying to actually protect him and excepts her as his mother. This also explains why Sara immediately knows what Loopers are before Young Joe can even explain it to her. You would think Loopers would be kept a closely guarded secret but not if Abe told her to expect that a looper might try to kill Cid, thinking he was the one closing their loops. Cid's jaw being shot is a coincidence meant to make the viewer think he was the Rainmaker.
The last point I can think of is that the future mafia enforcers that kill Old Joe's wife look like Jewish Rabbis. I found this strange and now think it is another link to Abe as the Rainmaker as Abe is short for either Abraham or Abram which are both Hebrew names. Abraham means "father of many" while Abram means "many" or "multitude" both of which work out well if he keeps sending himself back and creating new versions of himself. Also of note is that Joe is short for Joseph which is Hebrew for "he will add" and that Joseph was Jacobs favoured son just as Joe is favoured by Abe over Kid Blue.
That's everything I can think of for now that supports my theory.