The Kli Yakar writes, "Three levels are written here, one higher than the other. The first level is על אתכם ואשא נשרים כנפי, 'I carried you on eagles' wings.' This is like a parent who carries his nursing child, representing the time that Hakadosh Baruch Hu is the Father, and Bnei Yisrael is the child. Afterwards, it states, אלי אתכם ואביא, 'I brought you to Me.' This is when it appears that [Hakadosh Baruch Hu and the Jewish nation] are equal, like brothers on the same level. And then it states, ממלכת לי תהיו ואתם, 'And you shall be to Me a king...' This is when Yisrael are keviyachol like Hashem's king, as it states (Shmuel 2 23:3), 'ה ביראת מושל צדיק, 'A tzaddik rules [keviyachol] over Hashem.'"
The Kli Yakar continues:
"This is as the Midrash (Shir HaShirim Rabba 3:11) states on the pasuk, אמו לו שעטרה בעטרה, “It can be compared to a king who had an only daughter whom he loved immensely. At first, he called her בתי ‘my daughter.’ Later, he called her אחותי, ‘my sister.’ Then, זז לא מחבבה, his love increased until he called her אמי, ‘my mother.’ Similarly, Hakadosh Baruch Hu loves the Jewish nation, and He calls them בתי ‘My daughter’ and then אחותי ‘My sister. He doesn’t stop loving them until He calls them אמי, ‘My mother.’
"It seems that this Midrash isn't alluding to the levels of love that there are, because it begins with calling the Jewish nation a daughter, and then it calls them a sister. Doesn’t one love his daughter more than he loves his sister? Rather, the Midrash here refers to the degrees of rulership the Jewish nation has. A father rules over his daughter, while brothers and sisters are equals. Hakadosh Baruch Hu first calls Klal Yisrael "daughter" because of His love for the Jewish nation. But at that stage, Hashem rules over them, as a father rules over his daughter. This was in the days of Avraham...and this is the first level mentioned here, על אתכם ואשא נשרים כנפי, 'I carried you on eagle's wings.' It is like a father carrying his infant. Then Hakadosh Baruch Hu raises them to a higher level and calls them אחותי, My sister. This means they are equal to Hashem. [About this level, Chazal say that] Hakadosh Baruch Hu requires us to respect and to be in awe of the tzaddikim, similar to the degree we must respect and fear Hashem. When we are at this stage, tzaddikim become like partners with Hashem. This is how it was in Yitzchak Avinu's time because Hakadosh Baruch Hu told him (Bereishis 26:3) עמך ואהיה, 'I will be with you.' This means equal to you. This is because Yitzchak's merits were added to Avraham's merits. This is the reason Hashem didn't say to Avraham עמך ואהיה, 'I will be with you,' as He said to Yitzchak.
"This is the meaning of אלי אתכם ואביא, "I brought you to Me,' which is similar to ואהיה עמך, 'I will be with you.'
"Then, when Yaakov Avinu came, he acquired all three merits [his own, his father Yitzchak’s, and his grandfather Avraham’s], and Hashem raised him to an even higher level to call him אם, mother, like a mother who rules over her children. As Chazal (Moed Katan 16:) tell us [that Hashem decrees and a tzaddik annuls the decree]. Therefore, to Yaakov, Hashem said (Bereishis 32:29) עם שרית כי אלקים, 'You have commanding power with Hashem...' [which indicates that Yaakov rules keviyachol over Hashem]... This is implied by the words, ממלכת לי תהיו ואתם, meaning you will be like kings לי, over Me, Hashem. I decree, and a tzaddik annuls. Klal Yisrael also merits this because they are Bnei Yisrael [descendants of Yaakov Avinu]."
The nimshal is that when the Jewish nation was in Mitzrayim, they weren't aware of their greatness. But when they were about to receive the Torah, Hashem told them (Shemos 19:5-6) תהיו ואתם...העמים מכל סגולה לי והייתם קדוש וגוי כהנים ממלכת לי, “You will become My treasure among all nations... You will be a kingdom of princes, a holy nation.” Hashem showed them that they have tremendous potential. They aren’t simple people. They are the beloved royal nation. If they lift their wings, they will soar and reach the highest spiritual levels.
