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Cosmic dust is an essential component shaping both the evolution of galaxies and their observational signatures. How quickly dust builds up in the early Universe remains an open question that requires deep observations at (sub-)millimetre wavelengths to resolve. Here, we use Atacama Large Millimeter Array observations of 45 galaxies from the Reionization Era Bright Emission Line Survey (REBELS) and its pilot programs, designed to target [C ii] and dust emission in UV-selected galaxies at z ∼ 7, to investigate the dust content of high-redshift galaxies through a stacking analysis. We find that the typical fraction of obscured star formation fobs = SFRIR/SFRUV+IR depends on stellar mass, similar to what is observed at lower redshift, and ranges from fobs ≈ 0.3 − 0.6 for galaxies with log10(M⋆/M⊙) = 9.4–10.4. We further adopt the z ∼ 7 stellar mass function from the literature to extract the obscured cosmic star formation rate density (SFRD) from the REBELS survey. Our results suggest only a modest decrease in the SFRD between 3 ≲ z ≲ 7, with dust-obscured star formation still contributing ${\sim}30{{\ \rm per\ cent}}$ at z ∼ 7. While we extensively discuss potential caveats, our analysis highlights the continued importance of dust-obscured star formation even well into the epoch of reionization.