We study dimerization equilibrium between two dilute solutes in a supercritical solvent. Nonlocal hypernetted chain integral equation theory is employed to calculate the dimerization equilibrium constant for a wide range of solvent thermodynamic conditions and model potential parameters. The equilibrium constant displays a characteristic three-regime density dependence along near-critical isotherms, where it initially increases at low densities, decreases in the medium-density near-critical region, and increases again at high densities. The three regimes in the behavior of the equilibrium constant are discussed in terms of the energy-dominated low-density, desolvation-dominated medium-density, and entropy-dominated high-density regions.