Viral Gastroenteritis: This is the most common cause of watery diarrhea in infants and toddlers, often caused by rotavirus, norovirus, or adenovirus. The prolonged duration of 3 weeks could be due to a prolonged viral shedding or a secondary infection.

Lactose Intolerance: After a viral gastroenteritis, some children can develop a transient lactose intolerance, leading to continued watery diarrhea.
Toddler's Diarrhea: A common condition in toddlers characterized by chronic, watery diarrhea, often related to dietary factors or an immature gut.
Bacterial Infections: Though less common than viral causes, bacterial infections like Salmonella, Shigella, or Campylobacter can cause prolonged diarrhea in children.

Intussusception: Although it typically presents with bloody stools and abdominal pain, intussusception can occasionally cause watery diarrhea and is a medical emergency.
Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease or ulcerative colitis are rare in infants but can present with chronic diarrhea and would be critical to diagnose early.
HUS (Hemolytic Uremic Syndrome): Often associated with E. coli infections, HUS can lead to severe kidney failure and is a life-threatening condition.

Celiac Disease: An autoimmune reaction to gluten, leading to small intestine damage and chronic diarrhea, though it's less common to present for the first time at this age.
Congenital Chloridorrhea: A rare genetic disorder causing chronic diarrhea due to an imbalance of chloride and sodium in the gut.
Giardiasis: An intestinal infection caused by the parasite Giardia lamblia, more common in areas with poor sanitation or in children who attend daycare.