Weak current sensors are crucial for monitoring the insulation status and leakage prediction of power cables and equipment, playing a significant role in the construction of a visible, measurable, and controllable new power system. Conventional weak current sensors based on current transformers and fluxgate technologies exhibit issues such as large size and narrow frequency band. Tunneling magnetoresistive (TMR) chip-based sensor offers promising alternative, while it still struggles with low accuracy and poor anti-interference capability under complex power conditions. In this paper, we propose a non-invasive, high-precision, low-drift weak current sensor with mA-level resolution utilizing dual TMR symmetric structure to suppress the interference. When placed within a shielding box, it demonstrates a good linearity within the measurement range of ±300 mA, with an error of <1% and a resolution of <1 mA. Furthermore, a box-shaped shielding structure composed of three layers of silicon steel sheets is designed and optimized through finite element simulation, achieving excellent shielding effects in both simulation and actual measurements, with a relative error of <2% under geomagnetic interference. This TMR-based differential sensor, with its high accuracy, resolution, and strong anti-external magnetic interference capability, is suitable for real-time monitoring of weak currents in power, photovoltaic, and energy storage applications.