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The annihilation of heavy particles close to thermal equilibrium, which plays a prominent role in the chemical equilibration of heavy quarks in the quark-gluon plasma (QGP) as well as in many classic dark matter scenarios, is reexamined. We derive a scattering amplitude that resums near-threshold attractive interaction of the annihilating particles in terms of the nonrelativistic scattering T-matrix and Green's function, thereby capturing the pertinent Sommerfeld enhancement from both nonperturbative scattering state and bound state solutions. The derived formula is of such generality that it applies to arbitrary partial wave processes of two-particle annihilation, and enables us to incorporate finite widths of the annihilating particles. In a screened potential model, the nonperturbative scattering amplitude is computed and the Sommerfeld enhancement is identified for heavy quark-antiquark annihilation in the QGP. [ABSTRACT FROM AUTHOR]