If your two-week-old baby's eye is watery and sticky, but not red or bothering them, it could be due to a blocked tear duct. You can try gently massaging the area around the eye to help unblock it. If the eye becomes red or the discharge changes color, it's important to seek medical evaluation to rule out any infections or other issues. In the meantime, you can use moisturizing eye drops and warm compresses to help alleviate the symptoms.