I suspect you've just mis-stated what you intended to say.
In fact, the Constitution's 3/5 rule provided slave-holding states with many more representatives than their white populations alone could justify.
That's the root-source of the term "Slave Power" -- the South's increased political power in Federal Government resulting from owning millions of slaves.
In 1787, non-slave states only supported the 3/5's rule grudgingly, as a compromise to entice Southern states to join the Union.
But any suggestion that slaves somehow caused Southern states to pay higher Federal taxes is just ludicrous propaganda.