I'm guessing Zetsu is one of
Madara Uchiha's successful projects (created from First Hokage's DNA)!
And that makes me believe that
Obito and Zetsu must be knowing each other!
But on the contrary! When Tobi was searching Sasori's ring (after his fight with Chiyo and Sakura), if you observe Black Zetsu and White Zetsu's comments on Tobi, one would think that they weren't aware of Tobi's serious part of life.