Motivated by recent anomalies in flavor changing neutral current $b\to s{\ell }^{+}{\ell }^{-}$ transitions, we study $B_1\to B_2{\ell }^{+}{\ell }^{-}(\ell =e,\mu ,\tau )$ semileptonic weak decays with the SU(3) flavor symmetry, where $B_{1,2}$ are the spin-$\frac{1}{2}$ baryons of single bottomed antitriplet $T_{b3}$, single charmed antitriplet $T_{c3}$, or light baryons octet $T_8$. Using the SU(3) irreducible representation approach, we first obtain the amplitude relations among different decay modes and then predict the relevant not-yet measured observables of $T_{b3}\to T_8{\ell }^{+}{\ell }^{-}$, $T_{c3}\to T_8{\ell }^{+}{\ell }^{-}$, and $T_8\to T_8^{\prime }{\ell }^{+}{\ell }^{-}$ decays. (a) We calculate the branching ratios of the $T_{b3}\to T_8{\mu }^{+}{\mu }^{-}$ and $T_{b3}\to T_8{\tau }^{+}{\tau }^{-}$ decay modes in the whole $q^2$ region and in the different $q^2$ bins by the measurement of ${\Lambda }_b^0\to {\Lambda }^0{\mu }^{+}{\mu }^{-}$. Many of them are obtained for the first time. In addition, the longitudinal polarization fractions and the leptonic forward-backward asymmetries of all $T_{b3}\to T_8{\ell }^{+}{\ell }^{-}$ decays are very similar to each other in certain $q^2$ bins due to the SU(3) flavor symmetry. (b) We analyze the upper limits of $B(T_{c3}\to T_8{\ell }^{+}{\ell }^{-})$ by using the experimental upper limits of $B({\Lambda }_c^{+}\to p{\mu }^{+}{\mu }^{-})$ and $B({\Lambda }_c^{+}\to p{e}^{+}{e}^{-})$, and find the experimental upper limit of $B({\Lambda }_c^{+}\to p{\mu }^{+}{\mu }^{-})$ giving the effective bounds on the relevant SU(3) flavor symmetry parameters. The predictions of $B({\Xi }_c^0\to {\Xi }^0{e}^{+}{e}^{-})$ and $B({\Xi }_c^0\to {\Xi }^0{\mu }^{+}{\mu }^{-})$ will be different between the single-quark transition dominant contributions and the $W$-exchange dominant ones. (c) As for $T_8\to T_8^{\prime }{\ell }^{+}{\ell }^{-}$ decays, we analyze the single-quark transition contributions and the $W$-exchange contributions by using the two experimental measurements of $B({\Xi }^0\to {\Lambda }^0{e}^{+}{e}^{-})$ and $B({\Sigma }^{+}\to p{\mu }^{+}{\mu }^{-})$, and give the branching ratio predictions by assuming either single-quark transition dominant contributions or the $W$-exchange dominant contributions. According to our predictions, some observables are accessible to the experiments at BESIII, LHCb and Belle-II.