Self-mixing interferometry (SMI) is a promising sensing technology. As well as its compact structure, self-alignment and low implementation cost, it has an important advantage that conventional two-beam interferometry does not have, i.e., SMI signal fringe evolves into asymmetrical shape with increasing optical feedback level, which leads to discrimination of target movement directions for unambiguous displacement measurement possible by a single-channel interferometric signal. It is usually achieved by using SMI signals in moderate feedback regime, where the signals exhibit hysteresis and discontinuity. However, in some applications, e.g., in biomedical sensing where the target has a low reflectivity, it is hard for the SMI system to operate in a moderate feedback regime. In this work, we present comprehensive analyses on SMI signal waveforms for determining system parameters and movement directions by a single-channel weak feedback SMI signal. We first investigated the influence of two system parameters, i.e., linewidth enhancement factor and optical feedback factor, on the symmetry of SMI signals. Based on the analyses on signal waveform, we then proposed a method of estimating the system parameters and displacement directions. The method was finally verified by experiments. The results are helpful for developing sensing applications based on weak feedback SMI systems.