«أكرمتُ» reports that honoring occurred. In «أكرمتُ إكرامَ أهلِ الحسبِ», a cognate accusative specifies the kind of honoring; it adds information about the act rather than simply repeating it.
The relevant question is “What kind of act was performed?” The absolute object may also intensify a verb in other settings, but its role here is differentiation of the action’s type.