[aninhumer]

There's no binary relationship status that suddenly switches people from "casual chat" to "going out for beers". What makes inviting someone out for a beer expected and normal is that your relationship is one where you often invite them out for beer. That means if you've never done it before, it's probably going to be a little bit awkward regardless. (Unless there's a culture of inviting random new people for beer, which is not uncommon.)

But unless you're absolute strangers, I don't think many people are going to think "weirdo", they'll just be slightly surprised.