1540s, "thick, coarse, gross, not thin or fine," from French crasse (16c.), from Latin crassus "solid, thick, fat; dense," which is of unknown origin.
The literal sense always has been rare in English. The meaning in reference to personal qualities, etc., "grossly stupid, obtuse" is recorded from 1650s, from French. Middle English had cras (adj.) "slow, sluggish, tardy" (mid-15c.), also crassitude "thickness." Related: Crassly; crassness.