A resonance that has relatively high loss. An impedance plot will show a high dip at series resonance and low peak at parallel resonance, as compared to a strong resonance. Asymmetric resonances are generally weak.
If both a strong resonance and weak resonance are near the nominal operating frequency of the power supply, then the power supply will normally run at the strong resonance. However, the weak resonance may still influence the performance of the strong resonance.