stalk (n.) Look up stalk at Dictionary.com
"stem of a plant," early 14c., probably a diminutive (with -k suffix) of stale "one of the uprights of a ladder, handle, stalk," from Old English stalu "wooden part" (as of a harp), from Proto-Germanic *stalo; related to Old English steala "stalk, support," and steall "place" (see stall (n.1)).
stalk (v.1) Look up stalk at Dictionary.com
"pursue stealthily," Old English -stealcian, as in bestealcian "to steal along," from Proto-Germanic *stalkojanan, probably from a frequentative of the root of steal (cf. hark from hear, talk from tell). Or it may be from a sense of stalk (v.1), influenced by stalk (n.). Meaning "harass obsessively" first recorded 1991. Related: Stalked; stalking.

A stalking-horse was literally a horse trained to allow a fowler to conceal himself behind it to get within range of the game; figurative sense of "person who participates in a proceeding to disguise its real purpose" is recorded from 1610s.
stalk (v2.) Look up stalk at Dictionary.com
"walk haughtily" (opposite meaning of stalk (v1.)) is 1520s, perhaps from stalk (n.) with a notion of "long, awkward strides," or from Old English stealcung "a stalking," related to stealc "steep, lofty."