Scaling concepts have been successfully applied for many years to synthetic polymers, but application to biology seems under-studied even though cells and tissues are built from polymers. Tissues such as brain and fat are very soft while tissues such as muscle and bone are stiff or even rigid, but the effects on cells are just now being discovered. Having shown that matrix stiffness helps specify tissue lineages in vitro, we used mass spectrometry to quantify protein levels in embryonic, mature, and cancerous tissues and studied tissues as well as cells on gels while tuning stiffness. Extracellular collagen polymers directly determine tissue stiffness with near-classical scaling, and for embryonic heart, contractile beating of the organ and of isolated cells on gels is maximal when the stiffness is that of the normal tissue, consistent with a ‘use it or lose it’ mechanism. Acto-myosin assembly likewise increases with stiffness and stresses the nucleus, which upregulates a nuclear structure protein called lamin-A (related to keratin in fingernails) that again scales with stiffness via ‘use it or lose it’. Lamin-A assembly has evolved to control nuclear plasticity and is known to vary widely between tissues and diseases including cancer. Differentiation of various stem cell types is generally modulated by lamin-A levels downstream of matrix stiffness, with various pathways co-regulated by lamin-A. Complementary insights from cell migration are obtained for DNA damage and repair factor mis-localization with stem cells and cancer cells, with evidence of invasion-mutation providing insight into mutation scaling in cancer.