Mijo used by people other than parents
My grandmother always called me "mijo" as do my aunts and some of my uncles and even some of my cousins. Mi abuela was mexican born and used the word commonly to anyone whom she cared about. I just take it to mean "loved one". Particularly family members.
It is also short for mi hijo-my son/child.
Look at this link: http://www.spanishdict.com/translate/mijo
It seems to be usual in Mexico... An old friend of mine call me that way... In Argentina I heard m'ijo/a many times but when I was a little girl, especially by old people. But now... not anymore.
Hope it helps!
English also allows this too if you think about it. Sometimes in elders, especially in storybooks, will say "my child" to people much younger than themselves.