Nasolacrimal Duct Obstruction: This condition is the most common cause of excessive tearing in infants. The nasolacrimal duct may not be fully open at birth, leading to a blockage that prevents tears from draining properly. It is usually a benign condition that often resolves on its own within the first year of life.

Conjunctivitis: This is an infection or inflammation of the conjunctiva, which can cause excessive tearing. In a 1-month-old baby, it could be due to a viral or bacterial infection.
Foreign Body: A small object in the eye can irritate it and cause watering. Although less common in infants due to their limited mobility and interaction with their environment, it's still a possibility.
Allergies: Though rare in infants, allergic reactions to substances like pollen or certain products can cause eye irritation and watering.

Glaucoma: Congenital glaucoma is a rare but serious condition that can cause excessive tearing, along with other symptoms like photophobia and eye enlargement. It requires prompt medical attention to prevent vision loss.
Corneal Abrasion or Ulcer: These conditions can cause significant pain and watering. In an infant, they might be indicated by excessive crying or avoidance of light.
Dacryocystitis: An infection of the lacrimal sac can cause tearing, redness, and swelling. It's a serious condition that requires antibiotic treatment.

Tear Duct Anomaly: Besides obstruction, other anomalies of the tear duct, such as a fistula, can cause abnormal tearing.
Congenital Punctal Stenosis or Atresia: These are rare conditions where the puncta (the small openings at the inner corner of the eye through which tears drain) are either too small or completely blocked, leading to tearing.
Systemic Conditions: Certain systemic conditions can manifest with eye symptoms, including watering, though these would be extremely rare and likely accompanied by other significant symptoms.