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I swear I lived exactly as you described. My cousin made comments similar to those about my fiancé, but I let it slide for months. Eventually, I snapped and said, ‘This is my life, don’t question my decision.’ Now we’re not speaking, but I feel at peace. You shouldn’t let anyone have authority over your relationship.
I think you need to tell your cousin directly, just say, ‘This is my life, this is my decision’ and move on. To be honest, if I were in your position, I would keep some distance; it’s really annoying to talk like that all the time. If someone acted like this in a friend group, you’d react the same way anyway.
I think it’s good to be accommodating, but don’t be too passive. You could say something like: ‘I value your opinions, but I’m feeling a lot of pressure on this. Please respect my decisions.’ That way, you won’t look bad to the family, and your cousin will understand your boundaries. 
Honestly, your cousin is probably saying this because they’re thinking of you, not out of bad intentions. I think you should accept that this is a common situation and not make it a big deal. Everyone feels the need to comment on our relationships. Maybe as they get to know your fiancé better, their bias will fade.
Why is everyone in the mindset of ‘I got uncomfortable, but I’ll just let it slide’? You’re literally accepting your cousin to decide instead of your fiancé. That’s irrational. Just say it directly, nobody should interfere in your life.
But is there perhaps something bad that she knows about your fiancé? If she’s constantly saying things like “you’ll regret it,” she might have seen or knows something. Why not have a private conversation to try to understand why she’s speaking so definitively?
Is your cousin jealous of your fiancé? I think there might be other reasons behind their interference; otherwise, everyone comments on every relationship, but it doesn’t get exaggerated. I think you should investigate what they might know about your fiancé’s past.
The main issue here is actually boundaries. Clearly, your cousin wants you to be okay, but this way of expressing it is not healthy. You need to kindly yet clearly establish your boundary by using language like, ‘I feel uncomfortable, and I don’t want to continue like this on this topic.’ It’s also important to manage how this reflects on the family carefully.
Let me add something; I’m sure my cousin saw something serious because he keeps saying, ‘I’ve heard things like this in a friend group.’ But he doesn’t give any details, so I’m a bit suspicious, to be honest. Maybe I should push him a little harder to talk about it?