I'm 27 weeks pregnant and my stomach just started to tighten up a lot is that normal ?

Yes. You are probably having braxton-hicks contractions; kind of like your uterus doing exercise to get in shape for labor. They are normal. Please mention this to your OB at your next visit.
Most likely yes. You do not mention if it just feels tight or if it is in cycles. As the baby grows the muscles must stretch to match the babies increasing size. If it is coming in cycles that cause pain you need to see your OB doctor. If you are concerned about it you should always call your doctor.