Punishing my Twitter bully?

[Sadie]

How will my twitter bully be punished?
What kind of lawsuit or criminal charges could a person face if they harassed someone on Twitter? I have been horribly treated by someone on Twitter. They have sent six increasingly nasty Tweets to me about my divorce and my child. The Tweets were not threatening but told me I deserved what life had given me. I have engaged with them and now want to find out who they are and seek some sort of retribution. What sort of charges would they face and what are my options? I know people in law enforcement who could help me and have some good money to support this.

I am willing to take this all the way, and I have friends who will make this a big deal to those who can help me. Does more influence equal better results?