The design of thin frequency selective surface (FSS) absorbers based on resistive films that meet the requirements of broadband, polarization independence, incident angle stability, and strong absorption is a challenging task. Fabrication tolerance of resistive film can result in fluctuations in sheet resistance, which negatively impact the absorber performance. To tackle these problems, this paper firstly investigates how sheet resistance fluctuations affect the absorbing performance of resistive film FSS absorbers. Through analysis of simulated current density distribution and impedance, it is revealed that the diversity of current paths provides an effective way to mitigate the influence of sheet resistance fluctuation. This is achieved by enabling flexible variation of surface current in response to sheet resistance fluctuates. Consequently, the variation of input impedance of the FSS absorber due to the fluctuation of sheet resistance is suppressed within a small range. Then, a method for bandwidth extension is proposed by employing the complementary variation of FSS impedance with frequency at different layers. By combining this approach with a miniaturization design, a thin and light FSS absorber is developed that exhibits ultra-wide bandwidth, polarization independence and angle stability while mitigating the effects of sheet resistance perturbation. The proposed FSS absorber achieves a 90% absorption bandwidth from 1.50 GHz to 20.50 GHz, covering Ku, X, C, S bands as well as part of the L and K bands, with a relative bandwidth of up to 173%. The absorber has a thickness of 0.093 λ<sub>L</sub> for both transverse electric (TE) and transverse magnetic (TM) polarizations, yielding a figure of merit (FoM, the ratio of the theoretical minimum thickness to the actual thickness) of 0.95, indicating that the thickness is close to the theoretical limit. The absorber retains over 90% absorption rate for TM polarization at an incidence up to 70° and 80% absorption for TE polarization at an angle of 45°. Furthermore, the 90% absorbance bandwidth of the absorber remains at 167.0% when the sheet resistance of any FSS layer fluctuates within a range from 12 Ω/sq to 30 Ω/sq. A prototype of the proposed FSS absorber is fabricated and measured, yielding experimental results that are in good agreement with the simulation results, thus validating the effectiveness of the proposed method.