What stops radio stations from playing heavy music?

A few months back, the rock music station in my city acknowledged that there was significant demand for them to start playing material from Stone Sour. However they said they wouldn’t be doing so, as it would push the boundaries of acceptability. They won’t play anything heavier than Metallica, and won’t explore newer heavy material.

Who decides what is too heavy for radio? This has nothing to do with bad language either. Few bands are better lyrically than Iron Maiden, but yet I have never heard them on the radio. Why do radio stations shy away from heavy music?