Do you think jealousy might be genetic?

Nah! I can't believe that. I would like to believe that it's learned. Kind of like racism.

Insecure people are often more jealous.  That could be a part of their personality .. or part of how they were raised.  It could be genetic .. or it just could be from their life's experience too.

Probably---as in part of a personality trait.

But jealousy does have a very logical component---the more important something is to you, the more likely you are jealous with regard to any rival for it.

No I think it is an acquired emotion when others give you pause to doubt your own worth:(

Not per se.  The inclination toward addiction is though.  Perhaps the behavior that an addiction to another person brings out could resemble jealousy. 

It's a bad habit that can be overcome just like anything else.