This will likely exceed your weight requirement, but many theaters sound-proof each theater with just drywall. Just going by memory from what my dad told me quite a while ago (he used to install drywall for a living, now he sells it) I believe they use about 12 1/2" layers of various densities, each density blocking/absorbing a certain range of frequencies. Now you don't need anywhere near as much sound-deadening as a theater does, so if you can find 1/4" thick drywall of a few various densities you should be able to build yourself a fairly good sound killing box.
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