Generally, it's a good idea to be well-acquainted with all roles. There is nothing worse than having someone who doesn't know what they're doing playing a role on some 450 champ that they only got so they could play draft mode a while ago, especially when they're your support. Being very good at Graves, an ADC, I'm sure you're familiar with that guy. Lol.
Any role can carry, but some roles are better for it than others under certain contexts. I'll do my best to put them in an order of easiest to carry with to hardest to carry with.
ADC - Very easy to carry with. ADC's have pretty much the highest lategame damage. They're easily blown up, but you have at least one person (the tank) whose job is pretty much to protect you in a teamfight. I mean, it's in the name for a very good reason.
Mid - Being a burst mage, typically, you should have plenty of damage to dish out. The only difference is that you very often times are much more ability reliant. Factor in that you can get over 1000 AP if you really want to build for it.... that's a lot of damage.
Junger - This one is harder to categorize. You can play tank junglers, or you can play assassin junglers. Assassin junglers are really good for carrying because of their high damage, and the unique ability to farm almost completely uninterrupted. You have to deal with no minion wave to stand behind, but you have to balance the ability to free-farm somehow, right? It's a little harder to know how to carry as a tank jungler, because your job in the late game is to take hits like a champ and hopefully dish out damage or cc. As a tank jungler, you job is more to facilitate kills in lane, which makes it easier for your team to take objectives.
Top - This one is almost always a tank, and, no matter how many times you kill an enemy, that won't always carry over to taking objectives better. If your adc deals no damage, then it's going to take a long time to take your opponent's towers, even if you're the most fed tank ever. The best way to carry as a top is to do the same as a tank jungler, but more in the spirit of using teleport to make other lanes a living hell for your opponents. If you're an assassin top like Fiora, do a good job, and you'll have the other team raging and arguing with each other so bad you'll keep getting kills and taking towers for pretty much free. This one is lower than jungle, because it's less common to have an assassin top than an assassin jungler.
Support - let's face it, supports are almost explicitly told not to ks, unless they're going to get away and you can safely pick up the kill. Unfortunately, being good can't always land you a win. Even if you are a master of playing Lulu support, that can't fix a horrible carry that dies all the time. Supports can have damage in the late game, but if you're so far behind out of the laning phase, you aren't scaling anything. You're too busy trying to save your towers. Know how to do this well so that the ADC's that know what's going on can win with you, but don't take support actively to try to climb in soloqueue. I know for a fact, some ADC's are beyond saving short of sending them to practice.
overall if you want some helpful picks for good champions in each role, just ask about a role or two and I can give you a few options, keeping in mind that you seem to be fond of playing Graves.