No duty free on the stop through North Carolina. Duty free only in Belize when going OUT of the country back into the US. Must show your boarding pass to get the duty free price. Duty free does not apply to entering Belize, only exiting the foreign country.
By the way,don't forget to bring your own food on the flight to Belize. The airlines do not serve anything more than a snack so either eat between flights or bring your food on the plane to eat.