The fossil record of cetaceans documents how terrestrial animals acquired extreme adaptations and transitioned to a fully aquatic lifestyle^1,2. In whales, this is associated with a substantial increase in maximum body size. Although an elongate body was acquired early in cetacean evolution³, the maximum body mass of baleen whales reflects a recent diversification that culminated in the blue whale⁴. More generally, hitherto known gigantism among aquatic tetrapods evolved within pelagic, active swimmers. Here we describe Perucetus colossus—a basilosaurid whale from the middle Eocene epoch of Peru. It displays, to our knowledge, the highest degree of bone mass increase known to date, an adaptation associated with shallow diving⁵. The estimated skeletal mass of P. colossus exceeds that of any known mammal or aquatic vertebrate. We show that the bone structure specializations of aquatic mammals are reflected in the scaling of skeletal fraction (skeletal mass versus whole-body mass) across the entire disparity of amniotes. We use the skeletal fraction to estimate the body mass of P. colossus, which proves to be a contender for the title of heaviest animal on record. Cetacean peak body mass had already been reached around 30 million years before previously assumed, in a coastal context in which primary productivity was particularly high.