We present deeper Chandra observations for weak-line quasars (WLQs) in a representative sample that previously had limited X-ray constraints, and perform X-ray photometric analyses to reveal the full range of X-ray properties of WLQs. Only 5 of the 32 WLQs included in this representative sample remain X-ray undetected after these observations, and a stacking analysis shows that these 5 have an average X-ray weakness factor of >85. One of the WLQs in the sample that was known to have extreme X-ray variability, SDSS J1539+3954, exhibited dramatic X-ray variability again: it changed from an X-ray normal state to an X-ray weak state within approximate to 3 months in the rest frame. This short time-scale for an X-ray flux variation by a factor of greater than or similar to 9 further supports the thick disc and outflow (TDO) model proposed to explain the X-ray and multiwavelength properties of WLQs. The overall distribution of the X-ray-to-optical properties of WLQs suggests that the TDO has an average covering factor of the X-ray emitting region of similar to 0.5, and the column density of the TDO can range from N-H similar to 10(23-24) cm(-2) to N-H greater than or similar to 10(24) cm(-2), which leads to different levels of absorption and Compton reflection (and/or scattering) among WLQs.