Exciton-phonon (EP) coupling in molecular aggregates is reexamined in cases where extended intermolecular interactions result in low-energy excitons with high effective masses. The analysis is based on a single intramolecular vibrational mode with frequency ω0 and Huang-Rhys factor λ2. When the curvature Jc at the exciton band bottom is much smaller than the free-exciton Davydov splitting W, the strength of the EP coupling is determined by comparing the nuclear relaxation energy λ2ω0 with the curvature. In this way, weak (λ2ω0⪡4πJc), intermediate I (λ2ω0≈4πJc), and strong I (λ2ω0⪢4πJc) coupling regimes are introduced. The conventional intermediate (λ2ω0≈W) and strong (λ2ω0⪢W) EP coupling regimes originally defined by Simpson and Peterson [J. Chem. Phys. 26, 588 (1957)] are based solely on the Davydov splitting and are referred to here as intermediate II and strong II regimes, respectively. Within the intermediate I and strong I regimes the near degeneracy of the low-energy excitons allows efficient nonadiabatic coupling, resulting in a spectral splitting between the b- and ac-polarized first replicas in the vibronic progression characterizing optical absorption. Such spectral signatures are clearly observed in OT4 thin films and crystals, where splittings for the lowest energy mode with ω0=161cm−1 are as large as 30cm−1 with a small variation due to sample disorder. Numerical calculations using a multiphonon BO basis set and a Hamiltonian including linear EP coupling yield excellent agreement with experiment.