Nugget, a diminutive of nug or nog, as logget is of log. “A nog of sugar” (Scotch) is a lump, and a “nugget of gold” is a small lump. So a “log of wood” is a billet (Latin, lignum), and “loggets” (Norfolk) are sticks of toffy cut up into small lumps.
A correspondent in Notes and Queries says nog is a wooden ball used in the game of shinney. Nig, in Essex, means a “piece;” and a noggin of bread means a hunch.