Using $e^+e^-$ annihilation data taken at the CESR collider with the CLEO-c detector, measurements of hyperon pair production cross sections and elastic and transition electromagnetic form factors have been made at the charmonium resonances: $psi(2S)$, $sqrt{s}=3.69$ GeV, $|Q^2|=13.6$ GeV$^2$, $mathcal{L}=48$~pb$^{-1}$; $psi(3770)$, $sqrt{s}=3.77$ GeV, $|Q^2|=14.2$ GeV$^2$, $mathcal{L}=805$~pb$^{-1}$; and $psi(4170)$, $sqrt{s}=4.17$ GeV, $|Q^2|=17.4$ GeV$^2$, $mathcal{L}=586$~pb$^{-1}$. %High efficiency particle identification has resulted in good statistical precision in the results. Results with good statistical precision are obtained with high efficiency particle identification. Systematics of pair production cross sections, and form factors with respect to the number of strange quarks in the hyperons are studied, and evidence is presented for effects of diquark correlations in comparative results for $Lambda^0$ and $Sigma^0$, both of which have the same $uds$ quark content.