The high incidence of Depression and Anxiety disorders among the JW's was always explained with the use of the scripture at Ezekiel 9:1-6 where it talked about the ones who were"sighing and crying" over the abominations of the world. They said it was to be expected that God's people would be more concerned and saddened by the wickedness going on around them, than the general population would be.
I think the Anxiety and Depression comes from knowing on some level that the beliefs don't quite add up and that they may be deluding themselves.