States do have a right to regulate marriage. I don’t think I would want my eleven year old daughter running off and getting married just yet.
No. Not a "right".
From the standpoint of the People, States do not have rights - States have powers. And, except where otherwise controlled by the U.S. Constitution, the States only have those powers granted by the People via each State's Constitution.
If the People of your State have granted the government of your State the power to regulate marriage, then your State has that power. If they have not, then it does not.