The recent experimental data of the weak charges of Cesium and proton is analyzed in the framework of the models based on the $mbox{SU}(3)_Ctimes mbox{SU}(3)_L times mbox{U}(1)_X$ (3-3-1) gauge group, including the 3-3-1 model with CKS mechanism (3-3-1CKS) and the general 3-3-1 models with arbitrary $beta$ (3-3-1$beta$) with three Higgs triplets. We will show that at the TeV scale, the mixing among neutral gauge bosons plays significant effect. Within the present values of the weak charges of Cesium and proton we get the lowest mass bound of the extra heavy neutral gauge boson to be 1.27 TeV. The results derived from the weak charge data, perturbative limit of Yukawa coupling of the top quark, and the relevant Landau poles favor the models with $beta =pm 1/sqrt{3}$ and $beta = 0$ while ruling out the ones with $beta= pm sqrt{3}$. In addition, there are some hints showing that in the 3-3-1 models, the third quark family should be treated differently from the first twos.
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