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.
Free persons, including free servants, plus three-fifths of other persons, excluding indians. For purposes of representation in the house and direct taxation. A direct tax is imposed directly upon property according to its value. A property or ad valorem tax. Of course, the Slave States gained an advantage because no such tax was ever imposed on property by Congress. After the Civil War, the category of other persons disappeared.