'Observe' means both 'to watch' and 'to comply' — dual senses present since Latin 'servare' (to guard).
To watch carefully; to notice or perceive; to make a remark; to comply with or celebrate (a custom, holiday, or law).
From Middle English 'observen,' from Old French 'observer,' from Latin 'observāre' (to watch, to watch over, to attend to, to guard, to keep), from 'ob-' (over, toward, in front of) + 'servāre' (to watch, to keep, to save, to protect). The Latin verb carried dual meanings from the start: 'to watch attentively' (as in observing the stars) and 'to keep or comply with' (as in observing a law or ritual). Both senses survive in modern English. Key
The dual meaning of 'observe' — both 'to watch' and 'to comply with' — is not a coincidence. In Roman religion and law, the same word described watching for divine signs (augury) and complying with the rituals they demanded. To observe the heavens and to observe the Sabbath are linguistically the same act: watchful attention that leads to proper conduct. The root 'servāre' also produced 'servant' and 'service' — those who watch and keep.