Resonant light pressure effects can open new degrees of freedom in optical manipulation with microparticles, but they have been traditionally considered as relatively subtle effects. Using a simplified two-dimensional model of surface electromagnetic waves evanescently coupled to whispering gallery modes (WGMs) in transparent circular cavities, we show that under resonant conditions the peaks of the optical forces can approach theoretical limits imposed by the momentum conservation law on totally absorbing particles. Experimentally, we proved the existence of strong peaks of the optical forces by studying the optical propulsion of dielectric microspheres along tapered microfibers. We observed giant optical propelling velocities ∼0.45 mm s−1 for some of the 15-20 µm polystyrene microspheres in water for guided powers limited at ∼43 mW. Such velocities exceed previous observations by more than an order of magnitude, thereby providing evidence for the strongly enhanced resonant optical forces. We analyzed the statistical properties of the velocity distribution function measured for slightly disordered (∼1% size variations) ensembles of microspheres with mean diameters varying from 3 to 20 µm. These results demonstrate a principal possibility of optical sorting of microspheres with the positions of WGM resonances overlapped at the wavelength of the laser source. They can be used as building blocks of the lossless coupled resonator optical waveguides and various integrated optoelectronics devices.