I don't quite understand what you are asking, but you can definitely say "A man is crying", and it doesn't have to mean he is crying a lot.

Thank you,Lydia. I didn't know that but somehow I doubted because I also thought that crying is more related to the sound emitted.

Technically when tears are rolling down the cheeks, that is weeping. Crying is more related to the sound emitted, like a shout or a deep groan. And you can have a cry of triumph just as much as a cry of despair, a cry of anguish, a cry of victory, etc. You can say "he cried out and shouted when he found out he was the winner". And if you are in deep distress, and yet there are no tears, but the emotion in your soul is in deep anguish, your soul is crying out (even if it is a cry that only God can hear). We have gotten used to saying 'crying' for 'weeping', so it is now common and accepted usage of the word, but technically the tears are 'weeping'.