What would cause my brakes to stick?

This is on a 97 corolla. I first noticed it about a month ago cause i noticed brake dust on my wheels so I changed both of my calipers and I thought that had fixed it. Recently though it slowly is coming back. It will drive fine most of the time but occasionally they will stick and cause major drag when going up hills. Also when on a slight incline vehicle will not roll in neutral so I know it is something to do with the brakes. Not sure if it would be master cylinder, brake booster, booster check valve. Any information is helpful. Thank You