What happened to the Seven Dwarven Rings?

[Rumil]

On the Dwarven rings, does anyone know whether one ring was given to each of the ancient houses of the Dwarves?

If so that may mean that there were three rings in Moria originally, one for Durin's kindred, and one each for the dwarves of Nogrod and Belegost who had fled there after their homes in the Ered Luin were destroyed during the War of Wrath. Perhaps this is one of the reasons that Balin went back to Moria, as someone should really have told him that Thrain's ring was lost to Sauron.

The other four would then have gone to the Eastern dwarves, who don't come into the tales much apart from sending reinforcements to the 3rd Age War of the Dwarves and Orcs. I guess at least some of the Eastern dwarves were ensnared by Sauron as at the end of the second age its implied that some dwarves did indeed fight for him.