Therefore the mass (weight is a different thing, through it is proportional to mass at a given constant gravity potential) of the data on a SSD isn't fundamentally different from a HDD - they both are caused by a change of internal energy without any change in the number of fermions. I'd expect data on SSD to have larger mass change because a charged capacitor always store more energy than a discharged one, while energy of magnetic domains is less directional and depends mostly on the state of neighbor domains - but I'm not sure about this part.
[1] Thanks stackghost.