My baby is 2 month 10 days old. her leftside eye become sticky & watery & she's not gaining wait still, is this necessary to give her food supplement?

Two questions: The eye issue represents a partially blocked tear duct. The weight gain problem may have many unrelated (to the eye) causes and both require your pediatrician's attention.

Eye: This eye problem is likely a clogged tear duct. Take a warm cotton ball and gently massage the inner eye by the nose. Most infants grow out of it. The weight issue is a problem and you should see the infants doctor. Do not give any supplements. Breast milk is best or formula.