Mazal Tov Richard, may you be zoche to build a bayit ne'eman b'yisrael with your zivug. Say hi to Lamb and Kayser :)
Some say this minhag exists as the tallit
represents is the chuppa. See Bet Yosef EH 61.1, Rema 55.1
There is a connection between wedding and tzitzit (Devarim 22:12-13), and Kol Bo states this minhag is to encourage Torah and Mitzvot to the couple.
There's also a source that the minhag is for the sake of tzniut. See Manhig Hilchot Eruvin V'Nissuin.
Lev Chaim 3:99 brings that it is to ward off ayin hara
Note, I wasn't able to check the last two sources yet. They are quoted on Halachapedia.
It does seem to be a sefardi custom, as well as among German Jewry, as according to the Machon Moreshes Ashkenaz (p.117 in the pdf). It seems some Ashkenazim have adopted this custom.