My HD7970 (3GB version, Sapphire GHz edition) reports 2GB of free memory too. It is quite normal to reports less memory than the total amount (OS and driver have to reserve some memory) however your value looks really too low for a 6GB version.
On older AMD drivers was possible to set the amount of memory reserved to OpenCL via a couple of env. variables. However, it is a features that has never been officially supported and I'm afraid it is not available anymore on the latest drivers.