ease (n.) Look up ease at Dictionary.com
c.1200, "physical comfort, undisturbed state of the body; tranquility, peace of mind," from Old French aise "comfort, pleasure, well-being; opportunity," of unknown origin, despite attempts to link it to various Latin verbs; perhaps Celtic. According to OED, the earliest senses in French appear to be 1. "elbow-room" (from an 11th century Hebrew-French glossary) and 2. "opportunity." This led Sophus Bugge to suggest an origin in Vulgar Latin asa, a shortened form of Latin ansa "handle," which could be used in the figurative sense of "opportunity, occasion," as well as being a possible synonym for "elbow," because Latin ansatus "furnished with handles" also was used to mean "having the arms akimbo." OED editors add, "This is not very satisfactory, but it does not appear that any equally plausible alternative has yet been proposed."

At ease "at rest, at peace, in comfort" is from late 14c.; as a military order (1802) the word denotes "freedom from stiffness or formality."
ease (v.) Look up ease at Dictionary.com
c.1300, "to help, assist," from Old French aiser, from aise (see ease (n.)). Meaning "to give ease, mitigate, alleviate, relieve from pain or care" is from mid-14c. Meaning "render less difficult" is from 1630s; the sense of "to relax one's efforts" is from 1863 (with up by 1907, earlier with a more specific sense in sailing). Farmer reports ease in a slang sense of "to content a woman" sexually, with an 1861 date. Related: Eased; easing.