Χαῖρε κεχαριτωμένη ὁ κύριος μετὰ σοῦ
Kaire: The imperative is either a salutation given to superiors or a command to rejoice which could be given by anyone to anyone. Both are appropriate in different ways, since in the order of nature the angel is Mary’s superior but is her inferior in the order of grace.
In the order of nature, the angel reveals the true character of superiority in two ways:
1.) Inviting to the enjoyment of goodness. The purpose of authority is to bring about the full possession of the common good, and rejoicing is the full possession of the good. Even among equals, the highest sort of equality is in the co-enjoyment of a common good.
2.) Concern for others. As Plato shows in Republic I, the ruler simply speaking is not concerned with his own benefit but with the good of the ruled. But the command to rejoice is one that is entirely desirous that the ruled should enjoy the good.
The angel, however, is speaking primarily in the order of grace, and so the sense of Kaire simply is that the angel is greeting Mary as a superior.
Mary’s superiority is established not just from the salutation but from the whole dialogue that Gabriel has with her, and the best illustration of this is to compare it to the dialogue the angel has with Zechariah immediately before he speaks to Mary. With Zechariah he is magisterial, lofty, and severe, but with Mary he is deferential and subordinate. While both Zechariah and Mary are afraid and ask identical questions viz. “How can this thing you say ever happen?” in response to Zechariah Gabriel asserts the dignity of his angelic authority, criticizes Z’s lack of belief, and declares that Z will be struck dumb, while he never mentions his dignity to Mary, doesn’t even suggest a criticism of her, and explains that her proof will be her pregnancy.
Mary’s way of speaking is even more striking. Whereas the norm in the Old Testament is for humans to refer to angels as “Lord” (Genesis 18 and 19, Joshua 5, Judges 2, 6, and 13), Mary explicitly distinguishes the Lord and the angel in “I am the handmaid of the Lord, be it done unto me according to your word”. She doesn’t say “I am your handmaid” or “You are my Lord”. She acknowledges her subordination to God but not to the angel, and the angel quietly backs out of the room.
Kecharitoménae: Much has been made of the word being the verb “to give grace” as a perfect passive participle, but the descriptions are usually a bit thin on how to get from a referring to Mary as “ingratiated” to referring to her as “full of grace”. My own sense is that the matter is both simpler and more profound: “Graced” is being used as a quasi-title just as “Christ” is.
Just as Jesus is anointed (“Christ”), Mary is ingratiated or graced. While Jesus is not the only one who was ever anointed (all priests, prophets and kings were, and continue to be) Christ is the paradigm and fulfillment of all anointing, and, in the same way, Mary is the paradigmatrix and fulfillment of grace. This is not to deny Christ is also a paradigm of grace, but the word Kecharitoménae can’t be said of him since it’s feminine.
The point of the “full of grace” is that she is the measure of grace in the same way that the perfect-10 is the measure of everything else. As is clear in the Fourth Way, among virtual quantities that can be more or less there is always some maximal, and Mary is that maximal in grace.