How can biblical counseling help my preaching?

Well, first of all, I am honored that you would ask the question. Who am I that I would give advice on somebody's preaching? Even though I've thought about preaching quite a bit, and I've preached a lot of really, really skill-less sermons, so I'm familiar with the category. Let me just give you the one, to listen to people's stories. Oh, for example, stories about what they heard from a sermon.

I can remember one of the more helpful stories I heard was when somebody came after me and said, "Oh, thanks so much for your sermon. I really appreciated it." I had a couple minutes to ask what he appreciated and his response was, "Well, to tell you the truth, I didn't hear anything you said because there was so much noise around me, but it looked like you were really into it. You seemed really enthusiastic about it." It was a helpful story. I was glad that I was enthusiastic about the sermon and I realized that God can use all kinds of things.

You listen to stories, you listen to typical questions. Tell me about the best things in your life. Tell me about the things that are hard. Tell me about the way that the Spirit of God is continuing to change you. Tell me stories of transformation, that it might look subtle from your perspective, but it's glorious from another. Tell me about your children. Bring me into your day at work. Listen to people's stories, and I suspect that would enrich your preaching.