We present the results of spectroscopic observations for z~6-7 bright Lya emitters (LAEs) identified with the ~25 deg^2 narrowband (NB) imaging data of the Subaru/HSC SSP survey. Our NB imaging data is about an order of magnitude larger than any other surveys for z~6-7 LAEs conducted to date. Exploiting the largest NB imaging data, we obtain 28 very bright LAE candidates with log(L_Lya) >~ 43.4 erg/s that are similar to Himiko and CR7. Our on-going Subaru/FOCAS optical spectroscopy have so far confirmed 6 out of the 28 candidates with asymmetric Lya lines, and our subsequent Subaru/MOIRCS NIR spectroscopy cover UV nebular emission lines, CIV1548, HeII1640, and OIII]1661,1666, for three very bright LAEs with the spectroscopic redshifts. Combining spectroscopic samples from our HSC and previous Suprime-Cam studies, we make the first census of very bright LAEs at z~6-7. We find that the number fraction of spatiallyextended (>~10kpc) LAEs is about 20% in the bright luminosity range of ~6-60 L_Lya*. We discuss the formation mechanisms of very bright LAEs at z~6-7with the number fraction in conjunction with Lya radial profiles and line ratios of the UV nebular emission.