I think the best place to look for advanced constructions like that would be a native speaker's style guide like the Harbrace Handbook. That's just a guess. My own understanding of grammar is often based on gut instinct, even after taking a graduate-level professional editing class. Instinct suggests to me that the comparison language you're asking about is based on quantifiers (that is, amount versus quantity, or rather, values with opposites).
In the examples you gave, "twice as much" and "twice as tall" are quantifiable (measurable) values that have opposites. "Size" does not lean in any one direction.
Keep in mind, you can also say things like "my dog is smaller than your dog," which would eliminate some of the confusion.
Here are some examples off the top of my head:
"My cat is twice as fat as your cat" (as ... as because "fat" is opposite to thin).
"I can run twice as far as you can" (as ... as again because "far" is quantifiable, and opposite of near).
"I am much younger than you" (than applies to comparative quantifiers; in other words, it's clear that one is different than another, in a definite direction).
"Our house is half the size of yours" (of is proper in this case, but all I can think is that it's because "size" is not quantifiable without a direction applied to it--of is the word that effectively puts our under yours as opposed to over it).
Let me try another example: "You can eat half the amount of cake I can eat."
In this case, of is again appropriate because "amount" does not indicate a direction or less than/greater than for the comparison. Of is necessary to make half apply to the word "amount." I think you would only use "of" with "half" and in no other case.
Sorry, I'm sure that was confusing, but it's the best I can offer.