This paper describes the behavior of voltage weak DC distribution systems. These systems have relatively small system capacitance. The size of system capacitance, which stores energy, has a considerable effect on the value of fault currents, control complexity, and system reliability. A number of potential definitions of voltage weak DC distribution systems are proposed. These definitions address the main characteristics of voltage weak systems. A small signal model of a general voltage weak DC distribution system is developed in order to observe sufficient conditions for system stability. This is achieved by analyzing the dominant poles. The source converters are modeled as droop-controlled current sources in parallel with their respective terminal capacitors. As constant power loads have incremental negative impedances, which affect the system stability, especially, in voltage weak system, ideal constant power loads with their terminal capacitors are included in the small signal model. A three-node voltage weak DC distribution grid is analyzed, as a case study, by implementing the developed small signal model. The effects on system stability by the values of system capacitance, cable inductance, and cable resistance are investigated using dominant pole placement. Likewise, the influence of proportional-integral regulators and droop coefficients of source converters on the stability of the system is examined. Finally, the three node DC distribution grid is developed in MATLAB/Simulink in order to demonstrate the influence of small capacitance on system stability. Moreover, effect of the rate of change of constant power loads on the system stability is simulated. These results are further compared and verified on a voltage weak DC experimental test bench with a 350 VDC bus voltage.