Follow Up Advice Question

Question to those in PE,

Backgroud: I had a final round at a MM fund 3 weeks ago. During my interview they said they would get back to me in 3-4 weeks. I sent a thank you note and the hiring manager replied basically saying thanks, great meeting you and as discussed we will get back to you.

Question: I was thinking about calling him to check in, asking where they are in the process, let him know I'm still very excited about the opportunity and ask if they would like any additional information as they look to make a decision. Do you guys recommnend calling in? If so when would be most appropriate? Would it in any way hurt my position?

Thanks