In the oil and gas pipeline industry, numerous small-diameter branch pipe fillet welds exist, which are prone to stress concentration because of diverse geometric shapes. The internal welding defects within these welds pose severe hazards to safe production. Specifically, the irregular geometry often leads to internal root defects where the weld metal fails to fully penetrate the joint or fuse with the base material (referred to as incomplete penetration and incomplete fusion). This study developed a GF-CF-GF (CF is carbon fiber, GF is glass fiber) sandwich composite reinforcement structure for pipe fittings with these specific internal defects (main pipe: Φ323.9 × 12.5 mm; branch pipe: Φ76 × 5 mm) through a combination of finite element analysis (FEA) and burst test verification. The inherent correlation between structural factors and pressure-bearing capacity was revealed by analyzing the influence of defect sizes. Based on FEA, the repair layer coverage should be designed to be within 400 mm from the defect along the main pipe wall direction and within 100 mm from the defect along the branch pipe wall direction, with required thicknesses of 5.6 mm for incomplete penetration and 3.2 mm for incomplete fusion. Analysis of the actual burst test pressure curve showed that the elastic-plastic transition interval of the repaired pipes increased by approximately 2 MPa compared to normal undamaged pipes, and their pressure-bearing capacities rose by 1.57 MPa (incomplete penetration) and 1.76 MPa (incomplete fusion). These results demonstrate the feasibility of the proposed reinforcement design, which has potential applications in the safety and integrity of oil and gas transportation.