High stabilizer does NOT cause cloudiness.

Low chlorine DOES cause cloudiness and is the likely source of YOUR problems. Of course, it could be something else:
100-reasons-for-cloudy-swimming-pool-water
Regardless: low chlorine in your pool WILL cause a problem soon, if it hasn't already. Add some NOW! A reasonable starting place on your pool would be 2 gallons (or (3) 96oz jugs) of PLAIN 6% household bleach.