OK, serious answer. In short, no it doesn't.
The iPod stores it's contents on a small hard drive. Hard drives store data by creating patterns in the magnetic field of the disk's surface, so no physical material is added or removed from the drive when information is stored or removed, hence no change in the mass (weight) of the drive.
Of course to store large amounds of data you do need a larger and heavier drive as the disk needs to have more surface area, which is why a 40GB iPod is heavier than a 20GB model. However a 40GB iPo is going to weigh the same whether full or empty.
(I can't believe I just wasted the time to write all that)