Would it be against the law for a 16-year-old girl and a 17-year-old guy to leave their state to get married in another state?

You both would have to have your parents written permission in almost any state to get married whether you ran away to do it or stayed in your own state to do it. You would have to find a state that would even marry underage without parents written permission. You would need to call your local marriage license places as well as probably every other state first before you should even consider running away.