From the meaning in golf (where the stymie ball blocks the other ball from "seeing" the hole), perhaps from Scots stymie, stimie (“person with poor eyesight”), from Scots stime (“the least bit”). Or from Scots styme (“tiny bit, glimmer”) as in se nocht ane styme (“not to see a glimmer (of something)”). If so, it is a doublet of stime.