I don't think they really weigh anything. The SRD list them as being of no appreciable weight, at least for magic rings. As someone wears a ring and necklace in real life, they don't weigh much at all. I usually forget I'm even wearing them. I necklace with a really big amulet might weigh maybe 1 pound but that's about it. Just track the gold cost and don't worry about it.
Well if we consider the $20,000 or so rings that men buy for women for this odd mating ritual I think we can just conclude that you buy a ring worth 80 gp and you're done. And it weighs as much as a single ring. Which is nothing.