'Sad' originally meant 'sated, full' — from PIE *seh- (enough). It sank from satisfied to sorrowful.
Feeling or showing sorrow; unhappy.
From Old English 'saed' (sated, full, heavy with food, weary, tired of), from Proto-Germanic *sadaz (sated, having had enough), from PIE *seh2- (to satisfy, to satiate, to fill to capacity). The root's original meaning was fullness — not lack but excess. A sated creature is heavy, slow, and disinclined toward further activity; the Old English 'saed' described a state of biological completion, not emotional desolation. The semantic chain from *seh2- runs through