Eyelid veins removal. What is the best option? (Photo)

For your baby, you will likely need to go see an oculoplastic surgeon to evaluate vision and recommend a treatment protocol. Best, Dr. Karamanoukian Los Angeles

In an adult, veins in the eyelids can be treated easily with laser or sclerotherapy.In an infant or child, treatment should wait until they are 8-10 years old. If you still want your infant to be treated, make an appointment to see a pediatric oculoplastic surgeon. 

Babies' skin is thin and many times these facial veins will disappear over time.  Drooping of the eyelids should not be due to the veins and there should be another cause.  I would not do any treatment for these veins.