(literary) to show interest in or favor toward someone; to look upon someone with appreciation or value. Literal meaning is to look at someone with the black pupils of the eyes centered, rather than showing the whites of the eyes.

Bright eyes that cast alluring glances; used to describe the beautiful, expressive eyes of a woman

(literary) your kind consideration or favors, used as a formal honorific

to look around; to cast side-long or lingering glances