Using 24.1 fb−1 of e+e− collision data collected with the BESIII detector at the BEPCII collider, the Born cross sections and effective form factors of the e+e−→Σ+Σ¯− reaction are measured. The measurements are performed at center-of-mass energies ranging from 3.510 to 4.951 GeV. No significant evidence for the decay of the charmonium(-like) states, ψ(3770), ψ(4040), ψ(4160), Y(4230), Y(4360), ψ(4415), and Y(4660), into a Σ+Σ¯− final state is observed. Consequently, upper limits for the products of the branching fractions and the electronic partial widths at the 90% confidence level are reported for these decays.