In a brief glance at an object or shape, we can appreciate a rich suite of its functional properties, including the organization of the object's parts, its optimal contact points for grasping, and its center of mass, or balancing point. However, in the real world and the laboratory, balance perception shows systematic biases whereby observers may misjudge a shape's center of mass by a severe margin. Are such biases simply quirks of physical reasoning? Or might they instead reflect more fundamental principles of object representation? Here we demonstrate systematically biased center-of-mass estimation for two-dimensional (2D) shapes (Study 1) and advance a surprising explanation of such biases. We suggest that the mind implicitly represents ordinary 2D shapes as rich, volumetric, three-dimensional (3D) objects, and that these "inflated" shape representations intrude on and bias perception of the 2D shape's geometric properties. Such "inflation" is a computer-graphics technique for segmenting shapes into parts, and we show that a model derived from this technique best accounts for the biases in center-of-mass estimation in Study 1. Further supporting this account, we show that reducing the need for inflated shape representations diminishes such biases: Center-of-mass estimation improved when cues to shapehood were attenuated (Study 2) and when shapes' depths were explicitly depicted using real-life objects laser-cut from wood (Study 3). We suggest that the technique of shape inflation is actually implemented in the mind; thus, biases in our impressions of balance reflect a more general functional characteristic of object perception.