she really shouldn't need any reason beyond that you don't want her to do it. Period.
I agree with OP, just keep saying you don't want it. I would suggest don't make excuses, that just gives her something to argue about; just tell her no.
Also, I don't think you're weird. Some parents are ok with this even from a young age, personally, I'm not. My kids started have 1-night sleepovers once they were 2+ and sleeping well. They've never stayed away more than three nights total and DS is now 5.5