means The state of being tight — taut, constricted, or lacking slack, whether in a muscle, a rope, a budget, or a chest gripped by tension.

from From "tight," which traces back through Middle English "tight" to an Old English form meaning dense or watertight, with cousins across the Germanic languages (compare German "dicht," dense or sealed). The "-ness" is the old Germanic suffix that turns a quality into a thing — so "tightness" is simply the noun-form of being tight, the condition of having no give.