Context. HBC 722 (V2493 Cyg) is a young eruptive star in outburst since 2010. Spectroscopic evidences suggest 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 where 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 BVRI JHK S 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 how the spectral energy distribution evolved 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 concluded that the first peak of the outburst in 2010 September was mainly due to an abrupt increase of 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 of 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 both in the first peak and the 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 could 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 the theory of Bell & Lin (1994). Our study of HBC 722 demonstrated that accretion-related outbursts can occur in young stellar objects even with very low mass disks, in the late Class II phase.