The invention relates to autonomously buoyant heavyweight foundations (1) for connection to an offshore plant for converting wind energy or solar energy into electrical energy comprising a solid plate (2), at least one fillable chamber (3) and attachment means (5) for a supporting structure (10) of a wind turbine or solar plant. These are characterised in particular in that the offshore plant can be simply anchored at a fixed location. To this end, the solid plate (2) has anchor plates (4) each having an attachment means (5) for connection to at least one bracing means (13) for connection to the supporting structure (10). The anchor plate (4) comprises at least one vertically oriented or substantially vertically oriented first plate 6 having the attachment means (5) and at least one horizontally or substantially horizontally oriented second plate (7). The first plate (6) is at least partially in the solid plate (2) so that the second plate (7) is covered by a region of the solid plate (2). The first plates 6 of the anchor plates (4) are first plates (6) transferring the tensile forces of the supporting structure (10) and the second plates (7) are plates exerting the pressure forces resulting from the tensile forces onto the solid plate (2).