We calculate the beam (B n ) and target (A n ) normal single-spin asymmetries in electron-proton elastic scattering from two-photon exchange amplitudes with resonance intermediate states of spinparity 1/2 ± and 3/2 ± and mass W ≲ 1.8 GeV. The latest CLAS exclusive meson electroproduction data are used as input for the transition amplitudes from the proton to the excited resonance states.For B n , the spin 3/2 resonances dominate by an order of magnitude over the spin 1/2 states. In general we observe cancellations between the negative contributions of the ∆(1232) and N (1520) across both beam energy and scattering angle, and the positive contributions of the ∆(1700) and N (1720), leading to a rather large overall uncertainty band in the total B n . At forward angles and beam energies E lab < 1 GeV, where the ∆(1232) dominates, the calculated B n tend to overshoot the A4 and SAMPLE data. The calculated B n compare well with the measured values from the A4 and Q weak experiments with E lab > 1 GeV.