The filings show insurers’ planned increases easily outpacing broader U.S. inflation, but shy of the much larger boosts some critics predicted.

For instance, the Anthem HealthKeepers Inc. plan offered by a unit of WellPoint Inc. WLP +1.19% said it would raise premiums by an average of 8.5% across its individual plans in Virginia, which cover about 110,000 people and are sold on the online insurance exchange set up by the health law, as well as directly to consumers.

The company says it needs to increase the rates to take into account the poorer health of uninsured people signing up under the health law this year and next, and their pent-up demand for services, as well as the costs of new fees under the Affordable Care Act.

Virginia is the first state to make rate proposals for 2015 public.