The C6D6 detection system coupled with the pulse height weighting technique is widely used for experimental measurements of the neutron capture cross section. The thickness of sample used in the experiment directly affects the neutron beam time and the reliability of the experimental data. In the present work, the comparison of lutetium (Lu) neutron capture reaction cross section experiment with different sample thickness were studied by the C6D6 detection system of the back-streaming white neutron beam line at China spallation Neutron Source (CSNS back-n). The light response of the detection system was simulated with the considering of the sample thickness by GEANT4 Monte Carlo simulation code. The 4th order polynomial pulse weight function for different samples was determined by using the above light response function. In the experiment, the high precision capture yield distributions in the resonance energy region were obtained by applying longer neutron time of flight distance and dedicated background measurements. The experimental resonance parameters were deduced by analyzing of the capture yield distributions with the R-matrix theory. By comparing the results of capture yield and resonance parameters between the two groups, it is found that the resonance curve of 1.06mm natLu sample changes due to its thickness effect, and there is a large gap between the experimental resonance parameters and ENDF/B-VIII.0 database. However, the experimental results of 0.206mm natLu samples can well reproduce the ENDF/B-VIII. 0 data.