Conde Petie, Zidane and Dagger feign marriage to pass through the village towards the Sanctuary, after which you're given a choice.
I personally don't bother marrying Quina and Vivi (one additional cutscene I can't be bothered to watch :P), I just let them sneak through because that's so much cooler anyway.
Which do you usually do if you're the kind of person who plays through the game several times?