Thrice shall pay for... what?

[Ibrîniðilpathânezel]

This is something that popped into my head during a long drive this morning. For some reason, the Eagles came to mind, specifically Gwaihir, which brought to mind a recent discussion concerning Gandalf's apparent "weight" after his rescue from Zirak-zigil. Before the gates of Mordor, after the Ring has gone into the fire and Gandalf asks Gwaihir to take him to find Frodo and Sam, he says, "Thrice shall pay for all, if you are willing."

Pay for what?

I have heard many debates as to whether or not Gwaihir is the King of the Eagles in the Hobbit, and this comment of Gandalf's alone would convince me that he is not. After all, if the various rescues and conveyances were to be considered part of a repayment for Gandalf having healed the wound of the Eagle King and Gwaihir was that King, then this would be the fourth time he came Gandalf's aid, not the third (and that isn't counting the help in the Battle of the Five Armies). If that is so, what debt was Gwaihir repaying? Is it some kind of Eagle honor thing, that the kin and/or vassals of the King owe the Wizard a debt for saving his life, or did something else happen? I've been going through various books looking for an answer, but danged if I can see one. Am I just missing this in my haste, or was it something left unanswered? Any thoughts?