ok so I was sorta right....
It is because you are right handed that your left is bigger. Your right arm is significantly stronger than your left, so because you used the same weight for both, even though they had a strength difference, your left arm had to compensate for weakness, so it gained mass. Your right arm was used to being worked with the amount of muscle it had, so it didn't need to get any bigger to support the weight. I know this goes against a lot of things you've probably heard, but use a heavier weight for the right than you do the left. They'll even out.