sensible adj.

late 14c., "meaning, signification, interpretation" (especially of Holy Scripture); c. 1400, "the faculty of perception;" from Old French sens "one of the five senses; meaning; wit, understanding" (12c.) and directly from Latin sensus "perception, feeling, undertaking, meaning," from sentire "perceive, feel, know."

This probably is a figurative use of a literal meaning "find one's way," or "go mentally." According to Watkins and others, this is from a PIE root *sent- "to go" (source also of Old High German sinnan "to go, travel, strive after, have in mind, perceive," German Sinn "sense, mind," Old English sið "way, journey," Old Irish set, Welsh hynt "way").

The application to any one of the external or outward senses (touch, sight, hearing, any special faculty of sensation connected with a bodily organ) in English is recorded from 1520s. They usually are reckoned as five; sometimes a "muscular sense" and "inner (common) sense" are added (perhaps to make the perfect seven), hence the old phrase the seven senses, sometimes meaning "consciousness in its totality." For the meaning "consciousness, mind generally," see senses.

The meaning "that which is wise, judicious, sensible, or intelligent" is from c. 1600. The meaning "capacity for perception and appreciation" also is from c. 1600 (as in sense of humor, attested by 1783, sense of shame, 1640s). The meaning "a vague consciousness or feeling" is from 1590s.

late 14c., sensitif, in reference to the body or its parts, "capable of receiving impressions from external objects, having the function of sensation;" also (c. 1400) in scholastic philosophy, "of or pertaining to the faculty of the soul that receives and analyzes sensory information;" from Old French sensitif "capable of feeling" (13c.) and directly from Medieval Latin sensitivus "capable of sensation," from Latin sensus, past participle of sentire "feel, perceive" (see sense (n.)). Also in early Modern English sencitive.

By 1520s as "of, connected with, or affecting the senses." With reference to persons or mental feelings, "keenly susceptible to external influences," especially "easily touched by emotion, readily wounded by unkindness" (but also "ready to take offense"), by 1816.

What is commonly called a 'sensitive' person is one whose sense-organs cannot go on responding as the stimulus increases in strength, but become fatigued. [James Sully, "Outlines of Psychology," 1884]

The mechanical meaning "so delicately adjusted as to respond quickly to very slight changes or conditions" is by 1857. The Cold War meaning "involving national security" is attested by 1953. Related: Sensitively; sensitiveness.

The purely physical sense, in reference to a living being, skin, etc., "having quick or intense response to sensation," is by 1808; it is preserved in sensitive plant (1630s, also in Shelley's poem), a legume which is "mechanically irritable in a higher degree than almost any other plant" [Century Dictionary]. 

Marijuana ... makes you sensitive. Courtesy has a great deal to do with being sensitive. Unfortunately marijuana makes you the kind of sensitive where you insist on everyone listening to the drum solo in Iron Butterfly's 'In-a-Gadda-Da-Vida' fifty or sixty times. [P.J. O'Rourke, "Modern Manners," 1983] 

As a noun, in mesmerism, "one who is sensitive to hypnotic influence," 1850; later "one in whom the sensitive facility is highly developed, an aesthete" (1891).