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To distribute or dispense something. A noun or pronoun can be used between "mete" and "out." It is the Supreme Court's job to mete out justice in a situation like this.
mete something out
to measure something out. She meted the solution out carefully into a row of test tubes. She meted out the cookies to each of them.
To distribute and apply a measure or judgment of something: The cook meted out small portions of soup to the soldiers. Our school principal metes out strict punishment to those who break the rules. The central office gathers information and metes it out to the departments that need it.