late 15c., “prompt to serve,” from Middle French obséquieux (15c.), from Latin obsequiosus “compliant, obedient,” from obsequium “compliance, dutiful service,” fromobsequi “to accommodate oneself to the will of another,” from ob “after” (see ob-) + sequi “to follow” (see sequel). Pejorative sense of “fawning, sycophantic” had emerged by 1590s. Related: Obsequiously; obsequiousness (mid-15c.).
Sequi- Latin for to follow
Seguir- Spanish for to follow