Millions of years of evolution have adapted spider webs to achieve a range of properties, including the well-known capture of prey, with efficient use of materials. One feature that remains poorly understood is the attachment disc, a network of silk fibers that mechanically anchors a web to its environment. Experimental observations suggest that one possible attachment disc adheres to a substrate through multiple symmetrically branched structures composed of sub-micrometer scale silk fibers. Here, a theoretical model is used to explore the adaptation of the strength of attachment of such an anchorage, and complementary mesoscale simulations are applied to demonstrate a novel mechanism of synergetic material and structural optimization, such that the maximum anchorage strength can be achieved regardless of the initial anchor placement or material type. The optimal delamination (peeling) angle is facilitated by the inherent extensibility of silk, and is attained automatically during the process of delamination. This concept of self-optimizing peeling angle suggests that attachment discs do not require precise placement by the spider, irrespective of adhesion strength. Additional hierarchical branching of the anchorage increases efficiency, where both the delamination force and toughness modulus increase with a splitting of the cross-sectional area.