You're right there is the same force pushing down on each side. But there's also an additional force in water pushing up. It's called upthrust. It's equal to the weight of displaced water. If the densities are different the samples with the same weight will have different volumes and different upthrusts.

This can be quite a useful phenomenon practically. Anyone who has learned to scuba dive will know that if you take a deep breath in from your air tank you increase your volume without changing your weight and will be able to slightly change your bouyancy and float upwards or downwards without moving your limbs. Submarines also use the same phenomenon.