We report measurements of the parity-conserving beam-normal single-spin elastic scattering asymmetries on and , obtained with an electron beam polarized transverse to its momentum direction. These measurements add an additional kinematic point to a series of previous measurements of on and provide a first measurement on . The experiment utilized the apparatus at Jefferson Lab with a beam energy of 1.158 GeV. The average laboratory scattering angle for both targets was , and the average for both targets was 0.024 37 ( GeV). The asymmetries are ppm for and ppm for . The results are consistent with theoretical predictions, and are compared to existing data. When scaled by , the dependence of all the far-forward angle () data from to can be described by the same slope out to GeV. Larger-angle data from other experiments in the same range are consistent with a slope about twice as steep.