It’s not like the grades are regulated or anything. It’s just a vague indicator of how much money went into a given game.

thankfully it lets me know what studios to avoid unless it becomes an internet sensation, but I think the AAA/AA studio thing is something the studios started with.

They are just production value. How good a game looks and sounds, which isn't necessarily related to how fun a game is.

Company size, probably. AAA = extremely bloated with more bureaucracy to get anything done and approved than most governments.