Specific molecular arrangements within H-/J-aggregates of cyanine dyes enable extraordinary photophysical properties, including long-range exciton delocalization, extreme blue/red shifts, and excitonic superradiance. Despite extensive literature on cyanine aggregates, design principles that drive the self-assembly to a preferred H- or J-aggregated state are unknown. We tune the thermodynamics of self-assembly via independent control of the solvent/nonsolvent ratio, ionic strength, or dye concentration, obtaining a broad range of conditions that predictably stabilize the monomer (H-/J-aggregate). Diffusion-ordered spectroscopy, cryo-electron microscopy, and atomic force microscopy together reveal a dynamic equilibrium between monomers, H-aggregated dimers, and extended J-aggregated 2D monolayers. We construct a model that predicts the equilibrium composition for a range of standard Gibbs free energies, providing a vast aggregation space which we access using the aforementioned solvation factors. We demonstrate the universality of this approach among several sheet-forming cyanine dyes with tunable absorptions spanning visible, near, and shortwave infrared wavelengths.