Hi upashu
I have heard that some women can become so nauseous in the first trimester and don't eat much, some may even lose weight in the first 3 months of pregnancy. Usually the second trimester is better, usually a woman is not nauseous and as tired in the second trimester.
I agree with Mommy 35, I'm sure if the doctor was concerned, he/she would do something.
Hopefully your wife picks up and enjoys the second trimester, and the rest of her pregnancy, as it is such an amazing journey for a woman to take. Fingers x'd for you.