We measured temperature and time dependences of magnetization of Al-1.0%Zn-4.2%Mg (ZM14), Al-2.6%Zn-3.2%Mg (ZM33), and Al-4.1%Zn-1.1%Mg (ZM41) (at.%) alloys after various periods of natural aging and peak-aged heat treatments. Abnormally enhanced diamagnetic contributions on the magnetization were observed for the as-quenched Al-Zn-Mg alloys for the first time. The enhanced diamagnetism observed in ZM33 and ZM41 were found to largely alter in natural aging, while that of ZM14 little changed. Since zero-field muSR is quite sensitive to the local magnetism, we would like to study electronic structure (local diamagnetism) of Zn-vacancy pairs/Zn-Mg-vacancy clusters. The results provide important information for industry to understand the complex precipitation phenomena of Al-Zn-Mg alloys and thus improve mechanical properties.