Abstract We study the enhanced sensing of weak anharmonicities in a gain-based cavity-magnon-waveguide coupled system. By dissipatively coupling the two subsystems through a mediating waveguide, the Hamiltonian of the system is tailored to be anti-parity-time symmetric. Unique to the gain condition, the eigenvalues exhibit two singularities with linewidth suppression, distinguishing it from gain-free systems. Under the gain condition, a counter-intuitive bistable signature emerges even at low drive powers. As the effective gain approaches a certain value, this bistability yields a significantly enhanced spin-current response of the magnon mode. Consequently, the sensitivity, quantified by an enhancement factor, is enhanced remarkably compared to the linewidth suppression scenario. Moreover, the high enhancement factor can be sustained over a broad gain-bandwidth and also retains large even when the coherent coupling becomes considerably strong. Based on the integrated cavity-magnon-waveguide systems, the scheme can be used for sensing different physical quantities related to the Kerr-type nonlinearity and has potential applications in high-precision measuring microwave-signal nonlinearities.