Innovative floating offshore wind turbine (FOWT) platforms that deviate from the conventional semi-submersible, spar, and tension leg platforms (TLP) have become increasingly common due to the need to tap into the high wind energy potential located in deeper waters. One example is the hanging-mass concept, in which a suspended counterweight stabilizes a positively buoyant floater. This work presents a two-dimensional, nonlinear, multi-body model used to assess the influence of the counterweight mass and the suspension line stiffness on the system’s global performance, using linear stability analysis and time-domain simulations to conduct a parametric study. For example, the counterweight mass has a strong influence on the amplitude of rotational degrees-of-freedom. Corresponding natural periods may occur within the linear wave energy range for suitable counterweight sizes due to this strong influence leading to undesirable motions. High-frequency multi-body modes are also dependent on both the line stiffness and counterweight mass, which may result in high relative motion amplitudes and slack lines in certain conditions. Finally, the parametric study results contribute to preliminary hanging-mass FOWT design recommendations.