means The main stem or stalk of a plant that supports its leaves, flowers, or fruit; also, by extension, the act of pursuing or following someone or something stealthily.

from Two strands twist together here. The plant-stem 'stalk' descends from Old English 'stalu' (an upright piece, a post), kin to the word 'stale' meaning a rung or handle. The hunting 'stalk' — to creep up on prey — comes from Old English 'stealcian,' meaning to walk warily or stride stealthily, related to 'stealc' (steep, lofty) and a cousin of 'steal.' The stiff plant and the stiff, careful gait may share an underlying sense of standing tall and stepping deliberately, though English happily lets the two meanings live side by side.