The rapid decarbonization of the logistics sector through electrified heavy trucks presents a significant challenge for existing electrical infrastructures, particularly at charging sites constrained by low-power grid connections. In this context, Battery Energy Storage Systems (BESS) have emerged as a promising solution, acting as an energy buffer to decouple high-power charging demands from the upstream network, thereby mitigating grid overload and ensuring system stability. This study investigates whether the BESS Vilion EnerCube (P1000C2089), a containerized solution featuring a 2089-kWh capacity and a rated output power of 1000 kW, can enable fast charging of heavy-duty and passenger electric vehicles at on-route stations even when the grid connection is limited to 500 kW. Two distinct architectural designs, a parallel grid-support integration and a series buffer configuration, are modelled and compared through 24-hour Matlab/Simulink simulations using Swedish-specific operational profiles, including the Scania 45 R heavy truck and the Volvo XC40 passenger car. Results show that the parallel configuration reduces BESS energy losses by over 98% (0.24 kWh vs. 14.23 kWh per day), limits the depth of discharge to 2.5% compared to 28% in the series case, and requires only four charging cycles per day versus ten, while the series configuration achieves higher conversion efficiency (97% vs. 91.2%) and provides additional electrical isolation. These findings provide a preliminary technical framework for the design of BESS-buffered fast-charging infrastructure under weak-grid constraints.