Well, I think everyone is a little uneven. It is just natural that one side of the body is usually a little stronger and bigger than another. Have you ever seen an ambidextrous baseball pitcher?
I think you need to include a little more information to help figure out the problem. Do you do any kind of sports or work that requires more work from the right side? Have you had someone analyze your form on barbell exercises to make sure your stronger side is not compensating for the weaker side? Have you had an injuries? I ask this because I broke my left humerus when I was in my teens. The arm is shaped a little different than the right. It functions fines, but it is shaped and moves slightly different than before the injury. Any injury to the right arm, shoulder, head, or neck could cause a problem due to injuries to the muscles, tendons, ligaments, bones, or even nerves.
The obvious course of action is to first make sure you are doing the same workload for both sides. Second, have a qualified person analyze your form on your lifts. Third, include more unilateral work and see if that helps the problem. Fourth, vary up the workout between the sides. One side may need a little more weight, more reps, less rest, or even more rest than the other sides.
Good luck with the detective work. I think you will just have to do some trial, error, and research to figure out what works best.