The long-term relaxation of a long-range interacting N-body system is generically described by the inhomogeneous Balescu-Lenard equation (BL), which captures the lasting effects of two-body resonances. Yet, BL is ill-posed in the presence of flat frequency profiles, i.e. within "over-resonant" systems. In that case, one must resort to "resonance broadening theory" to include the contributions from nonlinear effects -- neglected in BL -- to self-consistently regularise BL's (sharp) resonance condition. This internship focuses on exploring, analytically and numerically, the effect of resonance broadening in low-dimensional long-range interacting systems. For that purpose, we will focus on the model of classical Heisenberg spins evolving on the unit sphere withn different external profiles, in the limit of weak collective amplification. In practice, we will explore analytically the nonlinear origin of resonance broadening, using stochastic theory, emphasising the existence of anomalous scaling with respect to N. In parallel, we will use extensive numerical simulations with varying total number of particles and dynamical temperature, to explore the extent of resonance broadening, and its possible saturation. Ultimately, this program of research will offer new clues on the validity of the different quasilinear assumptions on which BL relies.