Causations are not necessarily one way. Inflammation causes disease, disease causes obesity (unhealthy people tend to move less), obesity causes more inflammation. Start anywhere in the circle.

  I don't believe there's actually any evidence for the 
  claim that inflammation is the root issue for most disease

I quote from a seven year old issue of Nature insight (http://www.nature.com/nature/supplements/insights/inflammati...):

  Inflammation forms the basis of many physiological and 
  pathological processes. Much is known about how 
  inflammation is initiated, develops and resolves over the 
  short term. But less is known about the causes and 
  consequences of chronic inflammation, which underlies many 
  human diseases. Recent studies have extended our 
  understanding of chronic inflammation and the cross-talk 
  that occurs between inflammatory responses and other 
  physiological and pathological 
 

This is common knowledge and has been for a long time.