There isn’t much of any correlation, except coincidentally in that most of the breeds selected for working closely with human beings in complex tasks are in the 35 to 75 lb range because that’s large enough to do something useful but not too large to be clumsy. Some of the toy breeds are very bright though.
I don’t think Competitive Obedience judges are the end all be all of dog intelligence assessors. What they are seeing are dogs that are the most successful at competitive obedience exercises, and that’s all. These exercises are pretty completely divorced from activities that make a lot of sense to a dog, consisting of things like walking on the left side of your handler with your neck perfectly lined up with the seam line of their pants, looking up adoringly but never touching the handler, and retrieving a dumbbell over a jump.
What these competitions measure is the ability of the dog to enthusiastically repeat arbitrary movements with exactitude over and over and over. Breeds that are food or toy motivated, high-energy, not easily bored by repetition, and desire to work closely with their person, are the breeds that consistently do well.
People who use dogs for various kinds of real work have much different standards. Quite a bit of modern work for dogs requires problem solving that a person cannot do, which is why we breed dogs to do it. Herding is an obvious example – the herding talent is inborn, yes, but so is problem solving. A dog may have to go out of sight, locate and gather the stock, and figure out how to get them back to the handler, without any further instruction than “go find 'em”.
Because herding dogs work closely with handlers they seem smarter than the breeds that do less human-managed work – they are bred to take instruction. But I don’t know if that’s really the same as intelligence. Sight hounds, for example, learn to set up a successful kill by using the best talents of each dog in the pack, and problem-solve at a dead run. They are unbeatable at what they do – and it is definitely learned as well as inborn. But they are normally ranked as the dimmest of the dim in the Obedience world, because they really don’t give much of a hang about pleasing people, and are typically pretty inert when not chasing something.
I’ve been fascinated with what dog intelligence is for a long time. It’s a lot more complicated than Psychology Today is capable of describing, that I know.