This may come as a shock, but there weren't any plates. Smith made it all up.
Well, that's an interesting topic in itself. There were several people who claimed he had
something physical. I'm tempted to think he actually did keep something covered in the house, because it's odd that so many people would describe them as physically existing. His wife complained he kept them on the table and she had to keep moving them out of the way to get her work done--a detail that cracks me up. She's also behind the church prohibition on tobacco, after she complained about cleaning the spittoons and around the spittoons, when church members would come visit. You know what they say, behind every great man...
So then the question comes, where does a farm boy get something that feels enough like metallic plates to pass for that, when felt under wraps or seen from a short distance? He apparently didn't need to get the whole set, since a couple people claimed things like: "A large portion of the leaves were so securely bound together that it was impossible to separate them." (see the previous link I posted for sources). So there could be a few leaves and the rest a solid block of wood, and that would also explain the lighter weight.
Martin Harris may have guessed it: "Of the thickness of plates of tin," though Orson Pratt said they were "Not quite as thick as common tin" and others said they were thinner, more like parchment.
Tin plates would be fairly available, since any small-town tinner would buy tin in flat sheets for making up into cups, pans, etc.
Another not-quite-so-available but even better option would be copper printing plates. Go here
http://www.coinnews.net/2010/07/28/...ered-in-heritage-boston-ana-currency-auction/ to see a late 18th century example.
There was a printer in Palmyra New York where Smith lived, the same one who would later print the Book of Mormon, so it's
possible for copper plates to be in the area, though I don't know what techniques the print shop used and if there actually were any.
Imagine a young man who wanted to find an ancient gold book, stumbling across a few discarded plates like that, with their strange backward writing. A little work with a needle or small nail, and you could have columns of reformed Egyptian. The problem is, at .08 inches, I don't think they'd flex like parchment--anyone handled them? But they'd be in the range of tin's thickness. And the whole book wouldn't necessarily need to be the same thing--enough copper sheets, plus tin sheets or even heavy leather for filler, with a sealed portion of wood...