If you were doing a scientific treatise on specific gravity and were trying to correlate it to hardness you would be in big trouble. Diamond has a S.G of around 3.4 or so and the main ore of lead (Galena) has one of around 7.5 or so. The lead has a hardness of about 1.5 and Diamond, well you know.
The basic properties that give a high S.G are usually quite different from those that make it hard.