Grain growth in planet-forming disks is the first step toward the formation of planets. The growth of grains and their inward drift leaves a distinct imprint on the dust surface-density distribution and the resulting surface-brightness profile of the thermal continuum emission. We determine the surface-brightness profile of the continuum emission using resolved observations at millimeter wavelengths of the disk around TW Hya, and infer the signature of dust evolution on the surface density and dust opacity. Archival ALMA observations at 820 micron on baselines up to 410 kilolambda are compared to parametrized disk models to determine the surface-brightness profile. Under the assumption of a constant dust opacity, a broken radial power law best describes the dust surface density, with a slope of -0.53 +/- 0.01 from the 4.1 au radius of the (already known) inner hole to a turn-over radius of 47.1 +/- 0.2 au, steepening to -8.0 +/- 0.1 at larger radii. The emission drops below the detection limit beyond ~60 au. The shape of the dust surface density is consistent with theoretical expectations for grain growth, fragmentation, and drift, but its total dust content and its turn-over radius are too large for TW Hya's age of 8-10 Myr even when taking into account a radially varying dust opacity. Higher resolution imaging with ALMA of TW Hya and other disks is required to establish if unseen gaps associated with, e.g., embedded planets trap grains at large radii or if locally enhanced grain growth associated with the CO snow line explains the extent of the millimeter-continuum surface brightness profile. In the latter case, population studies should reveal a correlation between the location of the CO snow line and the extent of the millimeter continuum. In the former case, and if CO freeze out promotes planet formation, this correlation should extend to the location of gaps as well.