Inverse weberites are of interest as geometrically frustrated magnetic materials due to their unique cation arrangement. We have synthesized nine isostructural materials that adopt the inverse weberite crystal structure, which consists of cross-linked kagome layers. These materials, having the general formula MIIMIIIF5(H2O)2 (MII = Co, Mn, Ni, Zn; MIII = Ga, Cr, Fe, V), were synthesized using mild hydrothermal conditions, which yielded phase-pure samples after optimization of the reaction conditions. Their crystal structures and optical, thermal, and magnetic behavior were characterized using single-crystal X-ray diffraction, UV-vis spectroscopy, thermogravimetric analysis, and measurement of the magnetic susceptibility and isothermal magnetization data, respectively. Three distinct types of magnetism were observed, including simple paramagnetism, antiferromagnetism, and canted antiferromagnetism; the last type is accompanied by a high frustration index fin the range 4.16-8.09. We demonstrated that the magnetic behavior of inverse weberites depends on the presence or absence of unpaired-electron-containing cations on the two distinct crystallographic sites, which can be employed for the prediction of the magnetic properties of other compounds in this rich and diverse family.