What could cause hair lose around dogs eye?

The "weep" is actually tears that are overflowing from the orbit and running down the dog's face. The tears can be due to over-production or insufficient ability to drain.

Excessive production can be due to infection, inflammation or cancer. Insufficient drainage can be congenital (certain breeds of dogs are known for this), infection, inflammation or cancer.

If your dog's eyes have always done this, the white part of the eye has no red streaks and the clear portion of the eye remains clear, I wouldn't worry about it too much. However, if this is new, there are red streaks on the white of the eye or the clear portion becomes cloudy, red or discolored, you need to take your dog to a veterinarian for examination and treatment.