To adapt to a wide range of physically demanding environmental conditions, biological systems have evolved a diverse variety of robust skeletal architectures. One such example, Euplectella aspergillum, is a sediment-dwelling marine sponge that is anchored into the sea floor by a flexible holdfast apparatus consisting of thousands of anchor spicules (long, hair-like glassy fibers). Each spicule is covered with recurved barbs and has an internal architecture consisting of a solid core of silica surrounded by an assembly of coaxial silica cylinders, each of which is separated by a thin organic layer. The thickness of each silica cylinder progressively decreases from the spicule's core to its periphery, which we hypothesize is an adaptation for redistributing internal stresses, thus increasing the overall strength of each spicule. To evaluate this hypothesis, we created a spicule structural mechanics model, in which we fixed the radii of the silica cylinders such that the force transmitted from the surface barbs to the remainder of the skeletal system was maximized. Compared with measurements of these parameters in the native sponge spicules, our modeling results correlate remarkably well, highlighting the beneficial nature of this elastically heterogeneous lamellar design strategy. The structural principles obtained from this study thus provide potential design insights for the fabrication of high-strength beams for load-bearing applications through the modification of their internal architecture, rather than their external geometry.