Thank you for this excellent question.
Botox to the crow's feet area weakens the outer portion of the orbicularis muscle which surrounds the eye. The weakened muscle diminishes the appearance of wrinkles in this area.
This muscle also has the effect of pulling down on the outer portion of the eyebrow. Weakening the muscle can elevate the outer a eyebrow which in turn will often pull up on some of the outer a eyelid skin.
Similarly, botox in the middle of the forehead can depress the eyebrows and sometimes make the skin of the upper lid look more redundant. Using botox we can and contour the shape of the eyebrow somewhat.
Because botox in these areas can alter the amount of skin in the upper lid I generally recommend that my patients be evaluated for upper eyelid surgery without botox in place to get a more precise sense of the correct amount of skin that needs to be removed.
I hope that this helps to answer your question.