Context. HBC 722 (V2493 Cyg) is a young eruptive star in outburst since 2010. Spectroscopic evidence suggests that the source is an FU Orionis-type object, with an atypically low outburst luminosity. Aims: Because it was well characterized in the pre-outburst phase, HBC 722 is one of the few FUors from which we can learn about the physical changes and processes associated with the eruption, including the role of the circumstellar environment. Methods: We monitored the source in the BVRIJHKS bands from the ground and at 3.6 and 4.5 μm from space with the Spitzer Space Telescope. We analyzed the light curves and studied the evolving spectral energy distribution by fitting a series of steady accretion disk models at many epochs covering the outburst. We also analyzed the spectral properties of the source based on our new optical and infrared spectra, comparing our line inventory with those published in the literature for other epochs. We also mapped HBC 722 and its surroundings at millimeter wavelengths. Results: From the light-curve analysis we conclude that the first peak of the outburst in 2010 September was mainly due to an abrupt increase in the accretion rate in the innermost part of the system. This was followed after a few months by a long-term process, when the brightening of the source was mainly due to a gradual increase in the accretion rate and the emitting area. Our new observations show that the source is currently in a constant plateau phase. We found that the optical spectrum was similar in the first peak and following periods, but around the peak the continuum was bluer and the Hα profile changed significantly between 2012 and 2013. The source was not detected in the millimeter continuum, but we discovered a flattened molecular gas structure with a diameter of 1700 au and mass of 0.3 M⊙ centered on HBC 722. Conclusions: While the first brightness peak might be interpreted as a rapid fall of piled-up material from the inner disk onto the star, the later monotonic flux rise suggests the outward expansion of a hot component according to a previously described theory. Our study of HBC 722 demonstrates that accretion-related outbursts can occur in young stellar objects even with very low-mass disks in the late Class II phase. This work is based on observations made with the Spitzer Space Telescope. Spitzer is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.