  Hexagonal antiferromagnets Cs$_2$Cu$_3$MF$_{12}$ (M = Zr, Hf and Sn) have
uniform Kagome lattices of Cu$^{2+}$ with S = 1/2, whereas
Rb$_2$Cu$_3$SnF$_{12}$ has a 2a by 2a enlarged cell as compared with the
uniform Kagome lattice. The crystal data of Cs$_2$Cu$_3$SnF$_{12}$ synthesized
first in the present work are reported. We performed magnetic susceptibility
measurements on this family of Kagome antiferromagnet using single crystals. In
the Cs$_2$Cu$_3$MF$_{12}$ systems, structural phase transitions were observed
at $T_t = 225$ K, 172 K and 185 K for M = Zr, Hf and Sn, respectively. The
magnetic susceptibilities observed for $T > T_t$ are almost perfectly described
using theoretical results obtained by exact diagonalization for the 24-site
Kagome cluster with $J/k_B = 244$ K, 266 K and 240 K, respectively. Magnetic
ordering accompanied by the weak ferromagnetic moment occurs at $T_N = 23.5$ K,
24.5 K and 20.0 K, respectively. The origins of the weak ferromagnetic moment
should be ascribed to the lattice distortion that breaks the hexagonal symmetry
of the exchange network for $T < T_t$ and the Dzyaloshinsky-Moriya interaction.
Rb$_2$Cu$_3$SnF$_{12}$ is magnetically described as a modified Kagome
antiferromagnet with four types of neighboring exchange interaction. Neither
structural nor magnetic phase transition was observed in
Rb$_2$Cu$_3$SnF$_{12}$. Its magnetic ground state was found to be a spin
singlet with a triplet gap. Using exact diagonalization for a 12-site Kagome
cluster, we analyzed the magnetic susceptibility and evaluated individual
exchange interactions. The causes leading to the different ground states in
Cs$_2$Cu$_3$SnF$_{12}$ and Rb$_2$Cu$_3$SnF$_{12}$ are discussed.
