It's not communicable from person to person, but it's certainly communicable from your environment to you.
edit: Is this such a controversial statement? Does it bear explanation?
What we eat is not solely a matter of willpower. It is influenced by what sort of food is available. It is influenced by what sort of food is easier or harder to obtain. It is influenced by how hungry we are. How hungry we are can be changed by how stressed out we are, or by what we ate yesterday, or last week, or how active we have been lately. It is even influenced by what we see others eat, what is culturally acceptable to eat.
So yeah - obesity isn't communicable from person to person like the flu is, but it is something that your environment has a huge influence on.