They tend to wear slightly more on one side due to a list of reasons you'll find on any motorcycle forum, but if yours is "significant" you may have lost a wheel weight (or all of them). If not time for a replacement, you might try re-balancing the tire.
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Japan drives on the left, so tires on the right side wear out faster.
This is especially true of Avon Cobra.
There are grooves left on the left side, but there are no grooves on the right side.