The reason can be many reasons, including genetics. An important factor to consider is that hypertrophy is what causes muscles to grow.
Ideal reps for hypertrophy are lower than for endurance. 6-12 reps at heavier weights are ideal for hypertrophy, while 15+ reps at lower weights are best for endurance. During hypertrophy, the size of the muscles enlarge due to specific training modalities.
Ii is possibly that your dominant arm being used more has negated the hypertrophy effect and cause more endurance, but without knowing you specifically, this is mere speculation, although possible.
It could also be nothing more than genetics, or possibly childhood development. Possibly during childhood development, one side built more muscle fibers than the other.
Fortunately, there is a solution. If you care more about symmetry, then you can work the larger side less than the smaller side and work the smaller side normally. As a fitness trainer I do not recommend to train the smaller size more and the bigger side normally, because you could risk overtraining. Instead, decrease the usage of the larger side. While this is likely to result in slower gains, they will be safer and more symmetrical gains.
- Do not use different weights on different sides of a barbell. This could result in injury.
- If you use two dumbbells, you could increase reps, but if you use different size dumbbells at the same time you could risk an injury or a muscle imbalance.
- One-arm exercises are the best way to do more on one side.
Hope these tips help!