A quick glance through the document finds that:
"The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States."
"No Tax or Duty shall be laid on Articles exported from any State."
"No Preference shall be given by any Regulation of Commerce or Revenue to the Ports of one State over those of another: nor shall Vessels bound to, or from, one State, be obliged to enter, clear, or pay Duties in another."
I am not sure whether any of those, or something else I missed, has the implication I described, although the last one comes close if "ports" is broadly defined.