Like most people I enjoy using this on a daily basis, as a fairly harmless insult...I've actually only just found out that it comes from the Cockney rhyming slang "Berkshire Hunt", meaning cunt.

So, does this make berk as offensive? Considering what it's alluding to?

What's particularly confusing me is that Berkshire is pronounced "Barkshire", so it doesn't even work. Fuck's sake.