What are chances or precedents of insurance company paying for breast reduction when breast size causes health issues?

Excellent, actually. Insurance typically covers breast reduction when it is used to relieve pain associated with having large breasts. You'll want to document the issues with your general practitioner and then seek consultations with a board certified plastic surgeon to discuss your options. Insurance companies tend to look for a removal of at least 500cc (each) to consider it necessary reconstructive surgery.