The stress quantification in the stress concentration area of pipeline plays an important role in pipeline life evaluation and safety prevention. Weak magnetic detection technology is an effective stress concentration detection method. However, the presence of hard spots on the pipeline can generate similar signals to those of defects, interfering with stress quantification. This paper establishes an analytical model for the magnetic signal detection of non-volumetric damage in pipelines, analyzing the effects of hard spots and stress on the magnetic properties of the pipe material. The signal characteristics of hard point and stress concentration area are studied under different excitation intensities, and the dual magnetic field stress detection method using strong and weak excitation is proposed to eliminate the interference of hard point on stress weak magnetic signal. Experimental verification of the theoretical research was conducted. The results show that under weak excitation, the magnetization intensity decreases with the increase of stress and hardness. The attenuation gradient of magnetization increases with the increase of stress and decreases with the increase of hardness. Under strong magnetic excitation, the magnetization decreases linearly with the increase of hardness and is not affected by the change of stress. The signal characteristic magnetic sensitivity coefficient is introduced to characterize the detection ability of non-volume defects under different excitation intensities. Under 10 kA/m excitation, the tangential magnetic sensitivity coefficient of magnetic signal increases from 1.54 to 25.87 with the increase of stress, and from 7.46 to 33.87 with the increase of hardness. Both stress and hard points have good recognition ability. Under a 30 kA/m excitation, the tangential magnetic sensitivity coefficient of the magnetic signal increases from 0.07 to 0.54 as stress increases and from 0.49 to 4 as hardness increases, with hard spots being well identified but low stress identification capability. Therefore, the use of strong and weak magnetic two-field detection method can eliminate the interference of hard point on stress detection.