לא מרבכם מכל העמים, "not because you are the most numerous amongst all the nations, etc.⁠" The premise underlying the verse is that seeing we have a principle that the glory of a king is manifest in the numerous legions he owns, and it would therefore be natural for God, the King of Kings, to command the most numerous legions as His people, this is not the case in the God-Israel relationship. His relationship to you is governed by the degree of fondness He has developed for you, a consideration outweighing considerations of numerical strength. This is why He chose you to be His special people as already mentioned in verse 6. You do not have officers or policemen in the celestial regions you are subservient to, only to God Himself. This is the meaning of being an עם סגולה i.e. under His immediate authority. This is why you must not err to serve idols in any shape or form (see Nachmanides on that verse).

I believe that the correct way to interpret the words: "not on account of your being the most numerous,⁠" refers to the reason God took us out of Egypt to make us His nation. The verse provides evidence that we were indeed the most numerous people at the time but this did not provide God with the motivation to take us out of there. Rather, He was motivated by feelings of a strong fondness so that even if we had been the least numerous nation He would still have taken us out of there. God loved us and wanted to keep His oath to the patriarchs.
The reason God felt compelled to state all this now in the fortieth year after the Exodus is that now Moses had referred to how numerous the people had become, i.e. "like the stars in the sky" (1,10). If so, and especially seeing that the numbers of the people had not changed since the Exodus, how could God say that He had taken us out because we actually were the least numerous, i.e. כי אתם המעט מכל העמים?

We may add further that the absence of a dot, dagesh in the letter מ in the word המעט proves this; had the letter מ in המעט been written with a dagesh I would have used this as confirmation that the people had indeed been the least numerous. However, seeing that it is written without such a dagesh, just as in the word המעט In Numbers 16,9 or 16,13, the word is not to be understood as confirmation of anything, rather as a supposition. The meaning of the line is: the word אתם refers to the spiritual level of the people, i.e. a very high level. Moses, resp. God is saying: "you who are numerically the smallest nation are yet on such a high spiritual level that instead of considering yourselves the most insignificant of all you are the most significant of all. Nonetheless, even considering your relative excellence, the reason the Lord took you out of Egypt was because of a feeling of love for you and in order to keep His oath to them.
Our sages in the Midrash (compare Rashi Pinchas 26,36) interpret the words: "for you are the smallest, etc.⁠" as ה מעט, "five families.⁠" The total number of families of the Jewish people was 65, i.e. five fewer than the 70 nations (families) enumerated in Noach after the dispersal of mankind subsequent to the Tower. The expression חשק is a variant of קשור and is found in that sense in Exodus 27,10 חשוקים כסף, surrounded by bands of silver (closely attached). These bands were firmly attached. The word in our verse indicates that the attachment between God and the Jewish people is permanent, extends beyond the death of the bodies of the individual Jews.

A Midrashic approach based on Chulin 89: the word לא מרבכם means "not because you boast of the fact that you are so numerous but, on the contrary, because you are unassuming, modest before Me do I relate to you in this manner. David referred to this in Psalms 136,23: "He remembered us because we were humbled, for His kindness is everlasting.⁠" This is the true meaning of: "for you are the least assuming of all the nations.⁠" God said: "at a time when I bestow greatness upon you, you belittle yourselves.⁠" When I granted greatness to Avraham, he said: "I am but dust and ashes" (Genesis 18,27). When I granted greatness to Moses and Aaron they said "who are we?⁠" (Exodus 16,8). When I bestowed greatness upon David, he said: "I am only a worm and not a man" (Psalms 22,7). The nations of the world do not react in this manner. When I granted greatness to King Nimrod he went ahead and said "let us a build a tower which reaches into heaven!⁠" (Genesis 11,3) When I granted greatness to Pharaoh he reacted by saying: "who is Hashem that I should listen to His instructions!⁠" (Exodus 5,2): When I granted great stature to Sancheriv, he responded by saying: "Who amongst all the gods of these countries has saved them from my hand that you (Chizkiyah) would think that the Lord can save Jerusalem from my hand?⁠" (Isaiah 36,20) When I granted greatness to Nevuchadnezzar he proclaimed: "I will ascend the highest places" (Isaiah 13,14). Chirom the king of Tzor said: "I am a god; I sit enthroned like a god in the heart of the seas" (Ezekiel 28,2).