There are so many factors that go into play it is difficult to diagnose a problem. The most common tend to be a "death grip" on the bars. Your dominant hand is stronger than the other one either causing your dominant hand to grip harder; or your non dominant hand tries to compensate and grips harder than it is used to. The thing is to try and be cognizant of it if and lighten up.

Saddle height and tilt could also be factors. Handlebar width and tilt can be factors. Stem length and rise can also be factors.