Some of the common side effects of taking GLP-1 agonist drugs include nausea, vomiting, constipation, diarrhea, heartburn, gastroesophageal reflux disease (GERD), and headaches. Usually, the side effects are temporary and may get better over time. Discuss with your healthcare team if you develop any of these side effects. Usually, eating small portion sizes and low-fat foods helps to relieve the side effects.