I think a new friend of my gf has an unhealthy obsession with my gf not sure how to go about saying something without upsetting my gf, it worries me?

Unhealthy how?: If this could be life or bodily threatening - don't worry about the risk of upset - help her!. If it is less dangerous, consider the choice of just watching and waiting - try to 'be there' for her if needed. Often the reason we can't think of a good thing to say is that there isn't one. I assume she's an adult. Think of her that way. If she's not, there's not much you can do anyway. Best!