The evolution of large organismal size is fundamentally important for multicellularity, creating new ecological niches and opportunities for the evolution of increased biological complexity. Yet little is known about how large size evolves, particularly in nascent multicellular organisms that lack genetically-regulated multicellular development. Here we examine the interplay between biological and biophysical drivers of macroscopic multicellularity using long-term experimental evolution. Over 600 daily transfers (~3,000 generations), multicellular snowflake yeast evolved macroscopic size, becoming ~2·104 times larger (~mm scale) and 104-fold more biophysically tough, while remaining clonal. They accomplished this through sustained biophysical adaptation, evolving increasingly elongate cells that initially reduced the strain of cellular packing, then facilitated branch entanglement so that groups of cells stay together even after many cellular bonds fracture. Four out of five replicate populations show evidence of predominantly adaptive evolution, with mutations becoming significantly enriched in genes affecting cell shape and cell-cell bonds. Taken together, this work shows how selection acting on the emergent properties of simple multicellular groups can drive sustained biophysical adaptation, an early step in the evolution of increasingly complex multicellular organisms.