18 year old son with BAV stenosis and ascending dilation

My son, now 18 years old, was born with a BAV with mild-mod stenosis, and mild reguritation.  He is seen yearly by a pediatric cardiologist.  His gradient and  reguritation have not changed much in these 18 years.  However when we went 2 weeks ago to the cardiologist, his ascending aorta was dilated at its largest part at 4.5cm. His root is at 3.5cm.  We are going back in 6 months to get a another echo, and see how things look.  I was told that 5cm. is the time to consider surgery.  He is a candidate for the "Ross Procedure", and would need his ascending aorta replaced as well.  This all came as pretty shocking news, since we were so used to hearing "no change", see you in a year.  He now is taking a beta blocker.  I am wondering if being on the Beta Blocker will keep the ascending aorta at 4.5cm, and how quickly does the ascending aorta progress?  He is suppose to up his dose in a few weeks.  Are there any other drugs that would help slow the progression?  I don't know if body size has anything to do with aorta size, but my son is 6'1", and weighs 200lbs.