I think that crying is a healthy sign. Emotions that are/have been repressed are not a healthy sign of emotional intelligence. I often feel sad about various things; sometimes when people cry over something that I don't find emotional, I think I must be very odd/strange or cold.
Music can often move me, and I will often cry listening to a beautiful piece of music, whether of modern or a classical style. Similarly, I find some books very emotional, and clearly remember sobbing my heart out when reading 'The Bridges of Madison County', but not on watching the film however! There have been other books that have had a similar effect, poetry too of course.
When my mother died in 1999, it was several weeks before I cried, I had to stop the car on the journey back from work and cry, and I would feel better afterwards.
I feel that the crying of grief is very different to the emotional connection with the written word, or with music, that results in tears.