We measure the binding energies of weakly bound Feshbach molecules formed between Na and Rb atoms in their lowest hyperfine Zeeman levels. We form molecules at the Feshbach resonance near 347.64 G and dissociate them by magnetic field modulation. We use the binding energies to refine the singlet and triplet potential energy curves, using coupled-channel bound-state calculations. We then use coupled-channel scattering calculations on the resulting potentials to produce a high-precision mapping between magnetic field and scattering length. We also observe 10 additional $s$-wave Feshbach resonances for Na and Rb in different combinations of Zeeman sublevels of the $F = 1$ hyperfine states. Some of the resonances show 2-body inelastic decay due to spin exchange. We compare the resonance properties with coupled-channel scattering calculations that full take account of inelastic properties.
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