From Old English 'waeccan' (to be awake, keep vigil) — originally 'to stay awake,' not 'to look at.'
To look at or observe attentively over a period of time; to keep under careful surveillance.
From Old English 'wæccan' meaning 'to be awake, keep vigil, watch,' from Proto-Germanic *wakāną (to be awake, to watch), from PIE root *weǵ- (to be strong, lively, awake). The original meaning was not 'to look at' but 'to stay awake' — a watchman watched not primarily by looking but by not sleeping. The visual sense of attentive observation developed from the core idea
The timepiece called a 'watch' gets its name from the night watchman's vigil. The earliest portable clocks (sixteenth century) were called 'watches' because they were used by night watchmen to mark the hours of their watch — the period of wakefulness when they guarded the sleeping city. The name stuck even after the timekeeping function separated entirely from the act of guarding.