I have hypothyroidism and despite a 1200 calorie diet + cardio 5x/week, I can't lose weight. 38.1 BMI any suggestions? Bp and cholesterol normal.

Difficult issue. I trust that you are taking replacement medication for thyroid deficiency and are meticulous about calorie count. Further caloric restriction would help and you should consult a dietitian to ensure adequate intake of essential nutrients while further reducing your caloric intake. I understand that further reducing caloric intake is easier said than done.
I'm sympathetic. I assume you have been put on thyroid replacement medication which has been adjusted by your doctor so that your thyroid deficiency is now corrected? If not, do that first. Otherwise, reduce your caloric intake to 1000 calories a day and stay the course every single day. No giving up. No binging. Investigate high fiber, low calorie foods that are filling (ie, fruits and vegetables).