I think Terry and Angela are both right.
While you can certainly wail and weep, and you can cry silently, I take the nuances of these words from their alternate meanings. To cry out is to make a loud noise, while a stone wall that exudes moisture (silently, of course) is said to weeping.
There is also the way these are used in idioms:
- My hearts weeps for him. (I feel a deeply profound sympathy and sadness for him.)
- My hearts cries out to her. (I feel an overwhelming need to communicate some strong emotion to her.)
- To "cry ones heart out" (to sob, wail, howl, and/or keen, bitterly and at great length)
So, I'd say that "crying" is generally louder and more outwardly forceful, while weeping is more internal and perhaps even more heartfelt.