Why is common law referred to as "at common law"?

The "at" is used to note the state of the crime. It was a crime at common law.

And really you are reading the "at" because many law books use standards dating back a few hundred years. So you will see a lot of sequencing and paraphrasing that may not seem "modern". That is just the norm.

I would think that current usage is more along the lines of "common law crime".

I think the reason is because back in the day in England there were different courts. There were common law courts, courts of chancery, ecclesiastical courts, and I think there was more but can't remember the names. Depending upon what you did wrong, you would be tried in whatever court had the jurisdiction, or maybe you could end up in more than one court for the same crime, I don't know. I would have to research that part, but anyway, I hope that was helpful.