The binary system RW Aur consists of two classical T Tauri stars (CTTSs). The primary recently underwent its second observed major dimming event (ΔV ∼ 2 mag). We present new, resolved Chandra X-ray and UKIRT near-IR (NIR) data as well as unresolved optical photometry obtained in the dim state to study the gas and dust content of the absorber causing the dimming. The X-ray data show that the absorbing column density increased from NH <0.1 × 1022 cm-2 during the bright state to ≈2 × 1022cm-2 in the dim state. The brightness ratio between dim and bright state at optical to NIR wavelengths shows only a moderate wavelength dependence and the NIR color-color diagram suggests no substantial reddening. Taken together, this indicates gray absorption by large grains (≳ 1 μm) with a dust mass column density of ≳ 2 × 10-4 g cm-2. Comparison with NH shows that an absorber responsible for the optical/NIR dimming and the X-ray absorption is compatible with the ISM's gas-to-dust ratio, i.e., that grains grow in the disk surface layers without largely altering the gas-to-dust ratio. Lastly, we discuss a scenario in which a common mechanism can explain the long-lasting dimming in RW Aur and recently in AA Tau.