stalk (v.1)youdaoicibaDictYouDict[stalk 词源字典]
"pursue stealthily," Old English -stealcian, as in bestealcian "to steal along, walk warily," from Proto-Germanic *stalkon, frequentative of PIE *stel-, possibly a variant of *ster- (3) "to rob, steal" (see steal (v.)). Compare hark/hear, talk/tell). In another view the Old English word might be from a sense of stalk (v.1), influenced by stalk (n.). Meaning "harass obsessively" first recorded 1991. Related: Stalked; stalking.

A stalking-horse in literal use was a horse draped in trappings and 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 etymology, stalk origin, 英语词源]
stalk (v.2)youdaoicibaDictYouDict
"walk haughtily" (nearly the opposite meaning of stalk (v.1)), 1520s, perhaps from stalk (n.) with a notion of "long, awkward strides," or from Old English stealcung "a stalking, act of going stealthily," related to stealc "steep, lofty."