A lightweight component is equipped with two cover layers, which are made of a wood material, and a filling disposed in between the layers after cutting everything to size, having an edge support including thermoplastic material. The edge support is anchored in both the first and second cover layers starting from the narrow side. Anchoring is achieved by bringing the edge support into contact with the respective cover layer and coupling mechanical vibrations into the edge support by a sonotrode engaging from the narrow side. The edge support at the same time is pressed against the cover layer such that, in the region of a transition between the thermoplastic material and the wood material of the cover layer, part of the thermoplastic material is liquefied and pushed into the cover layer material, thereby producing a positively engaged anchoring after hardening.