What could cause constant burping and not feeling hungry?

Constant burping.: Your constant burping could be a sign that you have acid reflux which is not under adequate control. I would consider adopting anti-reflux precautions, particularly avoiding caffeine, tobacco, and alcohol and avoiding any exacerbating foods. I would add Tums to your medicine regimen as needed. If the problem persists, then you may want to see your doctor for a trial of medications. Good luck.