It's possible that they were aggressively worn down, if they're gold. As far as I understand, if you wear a ring a lot, taking it off often, it can become thin in places, as evidenced by my grandmother's more popular rings in her collection. However, it's possible they were just made like that, because that's as much as could be afforded!
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Thin Ring Bands by: Amanda M
The bands are likely made of silver. One of the ways you can tell if a piece if made of silver , is if it bends easily, as silver is a very flexible metal. There may be no other reason as to why they're thin, other then, the conserve precious metal and make the rings cost efficient.