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AT2019wey (SRGA J043520.9+552226, SRGE J043523.3+552234) is a transient first reported by the ATLAS optical survey in 2019 December. It rose to prominence upon detection, three months later, by the Spektrum-Roentgen-Gamma (SRG) mission in its first all-sky survey. X-ray observations reported in Yao et al. suggest that AT2019wey is a Galactic low-mass X-ray binary (LMXB) with a black hole (BH) or neutron star (NS) accretor. Here we present ultraviolet, optical, near-infrared, and radio observations of this object. We show that the companion is a short-period (P < 16 hr) low-mass (< 1 Msun) star. We consider AT2019wey to be a candidate BH system since its locations on the L_radio--L_X and L_opt--L_X diagrams are closer to BH binaries than NS binaries. We demonstrate that from 2020 June to August, despite the more than 10 times brightening at radio and X-ray wavelengths, the optical luminosity of AT2019wey only increased by 1.3--1.4 times. We interpret the UV/optical emission before the brightening as thermal emission from a truncated disk in a hot accretion flow and the UV/optical emission after the brightening as reprocessing of the X-ray emission in the outer accretion disk. AT2019wey demonstrates that combining current wide-field optical surveys and SRG provides a way to discover the emerging population of short-period BH LMXB systems with faint X-ray outbursts.