"Seems to me, since the CDL is based on Federal standards, the weight limitations that require a CDL would have to be uniform throughout the United States, wouldn't they?"
That's It! To drive anything 26,001 lbs or bigger you need a CDL.
The Plates for the truck are a different story and vary by state, but I hear that is the next thing the feds are looking at making standard nation wide.
Here in Utah anything over 10,000 lbs must pass through the Port of Entry when you come up to one, so if your driving a Chevy HD3500 which is rated for 15,000 lbs you have to pass through the port. In Wyoming it is anything over 26,000 lbs.