Why is my baby opening her left eye less than her right?

You may be describing ptosis which is a droopy upper eyelid. There are many causes for ptosis in an infant. The most common is congenital ptosis. It may also be due to a growth in the eyelid such as a chalazion or hemangioma. It is very important to see an ophthalmologist with experience in this immediately because even if the cause of the droopy eyelid may be benign, having a partially closed eye in a child of this age can very rapidly lead to amblyopia and this must be dealt with.