Our Gemara in Amud Aleph tells us:
One interrupts his Torah study to carry out the dead for burial and to escort a bride to her wedding.
However, the Gemara naturally wonders how many people are required to give these events their appropriate due respect? Should an entire Bais Medrash empty out in order to celebrate a wedding or a funeral?
The Gemara qualifies this ruling: In what case is this statement said? Only where there are not sufficient numbers of other people available to perform these mitzvos and honor the deceased or the bride appropriately. However, when there are sufficient numbers, additional people should not interrupt their Torah study to participate.
The Gemara asks: And how many people are considered sufficient? Rav Shmuel bar Inya said in the name of Rav: Twelve thousand men and another six thousand men to blow horns as a sign of mourning. And some say a different version: Twelve thousand men, among whom are six thousand men with horns. Ulla said: For example, enough to make a procession of people all the way from the town gate [abbula] to the place of burial.
This is obviously a large amount. It is apparent from the commentaries and the poskim (Shulchan Arukh, Yoreh De'ah 361:1) that these definitions of sufficiency were referring to only the funeral and not the wedding. Furthermore, Rambam (Mishneh Torah, Mourning 14:9) quotes the first part of the halakha, that is, we suspend Torah study for funerals and weddings in order that there be a sufficient number of people, without quoting the numbers in our Gemara. This seems to indicate that the Rambam felt the numbers were exaggerated, or that the intention of the Gemara was to define the upper limits in reference to someone who deserved such great respect.
Regarding the wedding, we are left to our own devices to determine what is sufficient, or even more likely, no number is sufficient. So it would seem from Shulkhan Arukh (EH:65:1) where the idea of interrupting Torah study for a wedding is mentioned, without defining any sufficient number. (It is important to note though, the halakhic definition of dancing and bringing joy at the Hachnasos Kallah may be limited to the escorting of the chassan and kallah to the chuppah, and the chuppah itself. Since some poskim hold Chuppah includes the Yichud room (EH 55:1), then the obligation would apply from the Chuppah to the Yichud room as well, hence the popular custom of dancing and escorting the couple to the yichud room.) The actual obligation seems to be upon whomever sees the procession passing by (Chelkas Mechokek op. cit.), and possibly even if you are just aware of the date and time of the wedding (Bircas Shmuel op. cit.)
I think the extent of respect and joy we show toward a new couple and their wedding is an indication of how much we value shlom bayis and how we see the importance of joy in enabling shlom bayis. After all, nearly the same halachos apply to a funeral, but in that case we mark the occasion by mourning and eulogies. Even though a wedding is serious business we are commanded to bring joy and levity, not solemnity.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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