"Normal" is relative in pregnancy, especially in regards to weight. Some people loose, some people gain, some people stay the same through first tri. I lost a lot for the first 6 months because I had killer morning sickness, and then I gained 30 pounds in the last 3 months. My OB was perfectly fine with my weight. Your OB is really the only one who can tell you if your weight is okay for you or not.
at my 16 week appointment I had only gained 6lbs. I wasn't sick or anything. Buuuuut then the holidays happened, and when I went in for my AS at 18 weeks my weight gain went up to 11lbs. So 5lbs in 2 weeks. Whoops.
totally different for everyone - I wound up gaining 28lbs total and delivering at 39+6. But I have friends that have gained much more and much less than me and have had totally healthy babies, and gone back to their pre-pregnancy weight eventually, so really it's nothing to stress about. Just try to be as healthy as you can and let your body do what it's going to do.