Why do we say על ידי חופה וקידושין, mentioning chuppah first when kiddushin takes place before chuppah (nisuin)?
One I answer I saw here is:
In the berachah we are referring to the marriage that took place between Hashem (Chatan) and the Jewish people (Kallah) at Sinai. Hashem uprooted the mountain and with the suspended mountain above them He gave them the Luchot — Tablets — with which Eirusin — betrothal — was consummated (see Midrash Rabbah, Shemot 15:31)
Hence, when we speak of Hashem’s sanctifying His nation through Chuppah and Kiddushin, Chuppah is mentioned first because Chuppah — the Divine revelation which embraced the Jewish people — preceded the actual Kiddushin — betrothal — the giving of the Torah.
(תורה אור, מגילת אסתר דף צ"ח, ד)
This is actually discussed by the rishonim.
The Itur writes that the correct text is חופה בקידושין, just due to the rules of Hebrew grammar the ב is weak (i.e. a 'vet') and sounds like a vav.
The Rosh writes that we stress the Chupa in order to clarify that the wife is only permitted to the husband after Chupa.
The Mordechai and Taz write that the language is based on our practice of the couple going under the Chupa prior to kiddushin.
The phrasing of the bracha leaves it a bit tricky. It's non-linear.
- You prohibited betrothed women from anyone.
- But allowed fully-married women to their husbands. When we say fully-married, we mean hey had chupah [unlike "betrothed"] -- of course they also had kidushin previously.
But the stress here is the nisuin effects the permissibility, and the nisuin is symbolized by the chupah.