Glass-fiber-reinforced polymer composites are of interest for lightweight structural applications, including marine structures, where accidental low-velocity impact is an important design consideration. This study investigates the low-velocity impact response of polyester-matrix composites reinforced with 4 layers, 6 layers, and 8 layers of biaxial glass fabric. A progressive test program, designed according to the number of fabric layers, used increasing impact-energy levels to cover both an indentation-dominated non-perforating regime and complete perforation, with the transition toward complete perforation in each configuration guiding the energy range selected for the configuration with the next higher number of fabric layers. Instrumented drop-weight tests with a 16 mm hemispherical impactor were analyzed using force, displacement, velocity, and energy histories. At the highest fully non-perforating energy levels of 30 J, 60 J, and 100 J, maximum contact forces were 7.25 kN, 13.05 kN, and 17.45 kN, while absorbed energies were approximately 28.7 J, 54.1 J, and 95.3 J. At 40 J, 80 J, and 120 J, respectively, the composite series entered the transition regime, with complete perforation observed for some of the tested specimens. The investigated parameters showed different diagnostic values: some were sensitive to the impactor mass–velocity combination, whereas displacement, energy, and velocity histories more clearly reflected the change in impact regime. The progressive test campaign, extended up to complete perforation, provides a practical means of identifying the transition between impact regimes and establishing application-specific impact limits. For design purposes, components exposed to accidental impact should therefore incorporate an adequate margin below the experimentally identified transition energy range.