Credit: Denise Truscello/WireImage

North West is a tiny treasure! Kim Kardashian and Kanye West welcomed their little girl, nicknamed "Nori" about five weeks early -- and, a close source tells Us Weekly exclusively, the reality star and rapper's baby weighed in at 4 pounds, 15 ounces at birth. "She's tiny and perfect," another source tells Us. "She looks just like Kim -- with her dark hair and some of her features."

The first source adds that "Kim is breastfeeding," and that "the baby is healthy." Which is certainly a big relief for Kardashian, 32, and West, 36, who endured a frightening medical emergency when doctors at Cedars-Sinai Medical Center in Los Angeles delivered North prematurely on June 15. "Kim was scared," another insider reveals. "And the doctors had to assure her that even though the baby was early, she was ready."

Thankfully, after getting the all-clear from her medical team, mother and baby left the hospital after a week last Friday, and the happy family -- including West -- are settling in.

"They are both so in love with their little girl," marvels a pal.