Zeus is a thundercloud homie created and formerly owned by Big Mom, that she summoned from her left hand. It is a special kind of homie, as it received a soul fragment from Big Mom herself.
During the escape from Totto Land, Zeus was captured by the Straw Hat Pirates and forced to become Nami’s slave. However, it has seemingly accepted its new role, as it now lives inside her Clima-Tact. As a result of this, he has effectively become Nami’s newest weapon.
I think Zeus may be also acting as a spy for Big Mom (possibly unwittingly). Considering that he was made with a piece of Big Mom’s own soul, it wouldn’t be unreasonable to suspect that Big Mom can sense his location or exert some level of control over him. Zeus’s rebellious behaviors all occurred during Big Mom’s eating fit, when she has lesser control over the homies. Now that she’s regained her senses, I think that if she really wanted to, she could recall her own soul from Zeus.
However, it would be convenient for Zeus to remain with the Straw Hats, since Big Mom undoubtedly wants to get revenge. She could probably create another cloud homie with her devil fruit powers if she really wanted to.
*Theory by jobriq