Multi-piece golf balls containing a dual-layered core structure are provided. The core structure includes a small, heavy inner core (center) having a relatively high specific gravity, and a surrounding outer core layer. The layers of the core structure may have different hardness gradients. The center of the core comprises a metal material such as copper, steel, brass, tungsten, titanium, aluminum, and alloys thereof preferably dispersed in a thermoplastic polymeric matrix. Different plasticizers such as fatty acid esters may be used. The outer core layer is preferably formed from a thermoset composition such as polybutadiene. The resulting ball has high resiliency and good spin.