A golf ball is described that includes a spherical core, an inner cover or mantle layer, and an outer cover layer. A wide array of ionomeric materials are noted for use in the various cover layers. The mantle and the outer cover layers exhibit different Shore D hardness values and at least one of the layers includes a heavy weight filler material to enhance the interior perimeter weight of the ball. In several particular versions of the golf balls, the filler material is present in an amount of at least 10% by weight based upon the weight of the layer or layers within which the filler material is incorporated.