I just wanted to know, under what type of power can a guardian give permission for a minor of 16yrs to marry? Can it be done under the power of attorney form or does it have to be through court? Thank you!:)

I think what you might just be able to do is call or visit your local Marriage license Office and they can tell you how it applies. Because the person is under age the question of when emancipation occurs is the real base. If by giving your consent then if they marry they will be emancipated.

Guardianship generally gives you the rights to authorize anything. Unless the guardianship is limited.

But why would you give permission for a 16 yr old to marry? Are the couple going ot have a baby?

Power of attorney is not the authority for doing this.
Normally a guardian ( of course appointed by the court) would have that authority unless it is limited to only some areas.

So to appoint a new guardian, normally some issue has to be found with the old guardian or parent