I guess the actual analogy to tapes or CDs would be carrying around a pile of blank tapes vs tapes with recordings on them -- same weight, different amount of music
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Actually CDs are bit funny. Wouldn't the weight ever so marginally depend on the record? And actually compared to blanks it would have different weight. At least for commercially pressed ones. As there would be pits in the disc. I'm not sure if you account for all components that is acrylic, aluminium and polycarbonate.
For vinyl there would absolutely be a small weight difference, as there is actual physical grooves that gets cut in order for the record player to reproduce the sound you "entered" (more accurately, took away) into the groove.
> Wouldn't the weight ever so marginally depend on the record?
This raises an interesting point. It's very undesirable to have long sequences of all 0 or 1 in a digital stream that is being read subject to a lot of analog effects. You want the line to return to a known state. This is why simple serial communication protocol like RS-232 uses a mark bit, to synchronize the clock repeatedly to protect against drift.
It's possible -- and usually preferable -- to implement a digital coding in a way such that the average signal intensity is 50% and there are an approximately equal number of 0s and 1s physically speaking, with frequent crossings, regardless of the actual signal contents. Unsurprisingly, CDs do this on several levels, first permutating the stream into blocks with error correction, and then into a line coding that has regular transitions even if the stream is all 0/1. Though they're not guaranteed to literally have the exact same number of 0 and 1 bits across any content.