The grid-connected converter with grid-following control (GCC-GFL) for renewable energy sources has a risk of instability when integrated into the weak grid. This paper aims to investigate the dynamic interactions and stability characteristics of the GCC-GFL system. From a control system perspective, the mechanism of small-signal instability in the system is revealed through dynamic interaction analysis between the GCC-GFL and the weak grid. Meanwhile, a novel stability evaluation index is proposed based on the real and imaginary parts of the equivalent loop gain in a multi-loop control system. On this basis, the dominant loop of the control system leading to system instability is identified. Furthermore, quantitative analyses are conducted to investigate the stability region of the GCC-GFL, considering the influence of AC grid strength, steady-state operating points, and converter control parameters. Finally, the correctness and effectiveness of the proposed methods are verified by the impedance analysis method, the time-domain simulations, and the experiments, respectively.