Why does the groom place an opaque veil over his bride's face?

The father of the first Jewish family, Yaakov, was the victim of a last minute switch on his wedding night. His father-in-law, Lavan, substituted Leah, the older of his two daughters, for Rachel, the one whom Yaakov loved and worked for. Yaakov discovered the deception only after he had consummated the marriage with Leah. Yaakov, choosing to accept his mazal (fate), remained with Leah and later also married Rachel, the bride of his choice.

Why did the first Jewish wedding have to take place through deception?
Why did the first Jewish family have to come into existence in such an enigmatic and strange manner?

Leah represents Yaakov's mazal (fate). She is the woman whom Yaakov was destined to marry. Rachel represents choice. She is the woman whom Yaakov loved and chose to marry. The narrative portions of the Torah contain much more than simple stories.

The entire Torah is G-d's authorized living manual for today's world.

There is a profound message being taught here. When one gets married, although he thinks that he is marrying a Rachel, the one that he chose, there are bound to be unforseen surprises. One will discover, after the wedding that he has also married a Leah, who represents the unanticipated nature of one's spouse. This unforeseen nature, however, is exactly what one needs in a spouse.

When the groom veils his bride, he is stating in effect, "I will love, cherish and respect not only the 'you' which is revealed to me, but also those aspects of your personality that are hidden from me. As I am bonding with you in marriage, I am creating a space within me for the totality of your entire being, including what remains veiled."

Under the Chuppah the groom says to the bride, "You are sanctified to me with this ring …" What he means is that I can't attain my full potential of sanctity without you. However, the bride remains silent. Why does she not verbally acknowledge her groom's words and his gift? The Baal Shem Tov explains that under the Chuppah the bride has reached such an exalted and unprecedented level of sanctity (kedushah) that the world is not ready to hear her holy speech.

When the Moshiach comes, then the world will have reached its spiritual zenith, and only then the bride will speak under the Chuppah. It will be as the Prophet Yirmiyahu says, "There will be heard in the cities of Yehudah and in the streets of Yerushalayim, the sound of joy and the sound of gladness, the voice of the groom and the voice of the bride."