I experienced the opposite with my hair thickening and being much more healthy. I have had the greasy hair problem in the past though and the advice from my hairdresser helped - I would guess that it's washing your hair every day that's probably more the culprit - it over stimulates the oil glands as every time you wash your stripping of oil - a vicious circle.
I know it's hard not to wash it every day - try going a couple of day between and using a dry shampoo, make sure you only condition the very ends of your hair avoiding the first 2 inches from your scalp