I have no doubt at all that the Eagles were friendly toward Gandalf because of his affiliation with Manwe (since it seems that every time they show up, Gandalf is there and somehow involved). It's the nature of that particular comment that really puzzles me. "Twice you have borne me, thrice shall pay for all." He's been counting, which makes it seem (to me at least) as though there is some specific debt involved, to which he is referring, but which is never specified.
I kinda like the idea of it being a subtle way of saying that the Eagles' service to that particular servant of Manwe would be over, though.