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A weak vertical coupled-bunch instability with oscillation amplitude of the order of a few m has been observed in SPEAR3 at nominal vacuum pressure. The instability becomes stronger with increasing neutral gas pressure as observed by turning off vacuum pumps, and becomes weaker when the vertical beam emittance is increased. These observations indicate that the vertical beam motion is driven by ions trapped in the periodic potential of the electron beam. In this paper we present a series of comprehensive beam measurements, impedance-based stability analysis, and numerical simulations of beam-ion interactions in SPEAR3. The effects of vacuum pressure, gas species, beam current, bunch fill pattern, chromaticity, and vertical beam emittance are investigated.