I have the same problem and it started in my 30's but my hair is light..so I really sympathize with the anguish you feel over this.
I gained weight recently on a high protein diet and the hair on my chin tripled. The endocrine doctor said I had very high testosterone. Body fat can increase testosterone levels, I think I read that. He is thinking I am insulin resistant and I just bought the book the Insulin Resistance Diet (I normally never follow diet books) where anytime you eat a carb you have to match it with a protein so that your blood Sugar is always stabilized and it ends your food cravings so you eat less, lose weight, testosterone goes down and so does hair on chin. That's my hope anyway.