People with significant nausea and vomiting in the first trimester could certainly experience some weight loss, but given your low starting weight, I think that this is worth mentioning to your doctor.
Yeah, losing weight in the beginning stage of pregnancy is quite normal, usually during the first trimester, the women will lose about four to five pounds and it is normal. but you should not leave at it is, you should eat more foods, especially healthy foods with all needed fruits, vegetables and milk.