Kuzan likely has ulterior motives, but he is clearly helping Blackbeard as well. I mean dude infiltrated a former yonko crew to disable her crew members, likely stole a copy of her road poneglyphs and captured Pudding who can read them, all things needed for Teach to reach Laugh Tale
Maybe he wants to know the true story behind the void century after the Ohara incident and think helping Teach would help him accomplish that
Maybe he wants to know the true story behind the void century after the Ohara incident and think helping Teach would help him accomplish that