Brewer's: Babies in the Eyes
That is, love in the expression of the eyes. Love is the little babe Cupid, and hence the conceit, originating from the reflection of the onlooker in the pupil of another's eyes.
In each of her two crystal eyes Smileth a naked boy [Cupid].
She clung about his neck, gave him ten kisses, Toyed with his locks, looked babies in his eyes.
Heywood: Love's Mistress.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894