That's southern for "I pity you."
I do not like it when people bless my heart. I had so many people say that to me after my last child was born. There were three children under the age of four, and the littlest one was sick. A lot. And people clearly pitied me. And I don't like to be pitied - it implies weakness. Either that or it implies I'm an idiot for not figuring out birth control and health insurance. Whatever.
The problem is that it is always well-meaning. And you can't be mad when someone says it to you. But I always am, but then feel guilty for being mad. It's a vicious circle, I tell you.