Weird definitely exists. If you can’t form social connections well with pretty much everyone you run into, you’re weird. You can pontificate about the proper terminology but that’s the one society understands.
Simply because the sample of people we encounter socially is skewed towards the pro-social, and the ones we notice and remember, doubly so.
There's a lot more quiet, reserved, low-key people out there than we realise, and most of them aren't weird.
(Also plenty of pro-social, extrovert types who are weird AF, but that's a different topic.)
As a moderate introvert (handle social situations OK but need the down time to balance), I just find some people aren't worth the effort, and like to save my energy for those that are.
But the weird/normal axis, I'm a little less comfortable with (similarly "neurotypical"/"neurodivergent"). Fundamentally I dislike the idea of letting the most boring people claim normal, in a similar way to how LGBTQ and nonwhite folks don't like it when cishet or white people claim normal. Most of the people I most enjoy spending time with are ADD, ADHD or ASD, and all the better for it. It's not like these are even disabilities, they're just different ways of being.
I'm OK with the labels themselves as a broad, shorthand way of understanding personality types / ways of seeing the world, but I don't buy that no-label people are more normal.