Fast days, with the exception of Yom Kippur and Tisha B’Av, begin in the morning. Does that mean we can enjoy ourselves the night before? In particular, the Three Weeks, with the custom in memory of the destruction of the Temple of refraining from having parties, begin on Shiva Asar BeTammuz (this year observed on June 29). If the fast of Shiva Asar BeTammuz does not begin until the morning, maybe the restrictions of the Three Weeks do not either.
However, it seems that there is sufficient evidence to suggest that the “fast day,” with its character of solemnity and mourning, begins the night before even though the actual fast, the prohibition against eating and drinking, starts only in the morning. The Gemara (Ta’anit 12a) records a debate over when the fast begins. According to one opinion, you may not eat after you finish your last meal at night. According to another, and this is how the Shulchan Aruch (Orach Chaim 564:1) rules, you are permitted to eat until you got to sleep, but once you go to sleep for the night, when you wake up you may not eat even if it is not yet morning (unless you make an explicit condition before you go to sleep that you want to eat in the morning).
It seems that the fast actually begins at night. However, there is permission to eat until you go to sleep (but no later than dawn). Similarly, many believe that the “Aneinu” addition to the Amidah for fast days (“Answer us, Lord, answer us on our fast day…”) is recited even at Ma’ariv the night before the fast, although Ashkenazic custom is that individuals only recite it at Mincha. This seems to indicate that the fast day really begins at sundown, even if we are still allowed to eat.
Therefore, it would seem improper to hold a wedding the night of Shiva Asar BeTammuz because the fast day and the Three Weeks begin at sundown.
Adapted from Shiurei HaRav on Mourning and Tisha B’Av, based on the lectures of Rabbi Joseph B. Soloveitchik.