The Gemoro* says, that מר בריה דרבינא when he saw that the
רבנן were overly joyous at his son's wedding, took an expensive crystal dish and broke it. This made them change their mood.
Tosfos writes, this to be the source of the Minhag (Hl. Tisha B'av 560:2) for breaking a glass at a Chupa/wedding.
At the Chupa we use a cheap glass and no one is bothered
about the loss of this glass.
Harav Y.S. Elyashiv zt"l explained that there are two types of
1) It is done to actually reduce Simcha (no music during
the year etc.)
2) It is done just to remind us of the Churban even though it doesn't reduce the Simcha.
R' Elyashiv said the purpose of breaking the glass under the
Chupa is just as a reminder of the Churban and not to reduce the Simcha.
Some Poskim complain, that when the glass is broken instead of the music to start blasting etc. we should have a somber moment.
According to R. Elyashiv, the Minhag Haolam is Meyushav.