We present our new Atacama Large Millimeter/Submillimeter Array (ALMA) observations targeting [O iii]88 μm, [C ii]158 μm, [N ii]122 μm, and dust-continuum emission for three Lyman break galaxies at z = 6.0293-6.2037, identified in the Subaru/Hyper Suprime-Cam survey. We clearly detect [O iii] and [C ii] lines from all of the galaxies at 4.3-11.8σ levels, and identify multi-band dust-continuum emission in two of the three galaxies, allowing us to estimate infrared luminosities and dust temperatures simultaneously. In conjunction with previous ALMA observations for six galaxies at z > 6, we confirm that all the nine z = 6-9 galaxies have high [O iii]/[C ii] ratios of, ∼10 times higher than z ∼ 0 galaxies. We also find a positive correlation between the [O iii]/[C ii] ratio and the Lyα equivalent width (EW) at the ∼90% significance level. We carefully investigate physical origins of the high [O iii]/[C ii] ratios at z = 6-9 using Cloudy, and find that high density of the interstellar medium, low C/O abundance ratio, and the cosmic microwave background attenuation are responsible to only a part of the z = 6-9 galaxies. Instead, the observed high [O iii]/[C ii] ratios are explained by 10-100 times higher ionization parameters or low photodissociation region (PDR) covering fractions of 0%-10%, both of which are consistent with our [N ii] observations. The latter scenario can be reproduced with a density-bounded nebula with PDR deficit, which would enhance the Lyα, Lyman continuum, and C+ ionizing photons escape from galaxies, consistent with the [O iii]/[C ii]-Lyα EW correlation we find.