I'm not sure if there is any halachic basis for any of this, but I've seen at most weddings the chasan just wears the kitul over the suit jacket. At a few weddings though, particularly in Israel, many chasanim wear the kitul underneath their jacket. Any reason for this?
A friend of mine was told by his rebbe at Chofetz Chaim yeshiva in Queens that it's a personal Yom Kippur -- hence, wear the kittel, but not out in the open.
The Lev Ita and Yismach Lev brings down the one should wear something ontop of kittel.