We performed a search for WLQs in the spectroscopic data from the Sloan Digital Sky Survey Data Release 7 based on Kohonen self-organising maps for nearly 10^5 quasar spectra. The final sample consists of 365 quasars and includes in particular a subsample of 46 WLQs with equivalent widths W(MgII) < 11 A and W(CIV) < 4.8 A. We compared various properties of the WLQs with those of control samples of ordinary quasars. Particular attention was paid to selection effects. The WLQs have, on average, significantly higher luminosities, Eddington ratios, and accretion rates. About half of the excess comes from a selection bias, but an intrinsic excess remains probably caused primarily by higher accretion rates. The spectral energy distribution shows a bluer continuum at rest-frame wavelengths > 1500 A. The variability in the optical and UV is relatively low, even taking the variability-luminosity anti-correlation into account. The percentage of radio detected quasars and of core-dominant radio sources is significantly higher than for the control sample, whereas the mean radio-loudness is lower. The properties of our WLQ sample can be consistently understood assuming that it consists of a mix of quasars at the beginning of a stage of increased accretion activity and of beamed radio-quiet quasars. (Abstract modified to match the arXiv format)