Sounds like you're really being taken for granted and it's time for you to stop supporting her. It's hard to get all the details from a quick FML, but I hope you're not supporting her financially as well considering she's almost 30. Time to put your foot down if she won't be appreciative.

Maybe the cousin is making sure she launches. It's pretty obvious that you're not. Grow a spine, dad. Kick the soon-to-be 30 y.o. woman out of the basement for her own good.

We don't know what's gone on between you two since she was 13.

We probably don't want to know.

Really, Richard? That's a little too far - even for you....
But that's just me. Enjoy your Labor Day Wknd! :D

That's more on you than me.

I didn't say anything. I just let you use your imagination.

"we probably don't want to know" implies very heavily that the relationship is icky and you know it. You might want to remember that real people post these stories, before implying sick behaviour like that.

that's a big yikes. I'm so sorry

I feel like we need more info on this one.

stop supporting her and make her move out

Is her biological father still around? Maybe this is her way of not hurting his feelings by choosing you over him.

Surely she's given you more of a reason as to why? If not, tell her you feel hurt. She probably doesn't realise it's hurt you so much

First off, the tradition of giving the bride away is really outdated, as if the bride were just property rather than a woman who has chosen to get married. So anyone who actually wants to give their daughter, stepdaughter or any woman away is a patriarch who doesn't believe in female agency.
You're not the biological father, even if you've supported this young woman. Traditionally it would be the biological father. I don't know of any convention that dictates that a stepfather would be a logical replacement.
Anyway, it's her wedding not yours, so don't make it all about you.
And maybe take the time to sound her out as to the state of your relationship, since she's obviously not on the same page as you. It may just be that she's very close to her cousin, and that dates back further than your relationship, maybe she promised he could play that role before you even came into her life. Or maybe she doesn't appreciate your support as much as you think she should - she might hate your guts and just pretend to like you for the sake of peace and quiet until she can leave home. Whatever, there's obviously some kind of discrepancy that's worth investigating.