See below. Belching is the act of expelling air from the stomach through the mouth. It usually occurs when the stomach distends, or expands because of too much swallowed air. Belching releases the air to reduce the distention. You can also have a gas buildup in the stomach from bacteria working on food, which give up for gas. Anxiety can cause just about any physical symptom but it would be uncommon for anxiety to cause excessive belching. If your anxiety includes hyperventilating then that would be a good source of swallowed air, which then could lead to belching. Some things that may help in belching. Tried to be aware of how much air swallowing. Try to chew food completely before swallowing it so that the stomach will have smaller particles for the bacteria to give off gas with. Excessive exercise can also lead to belching. And sometimes relief can be obtained with anti-acids; H2 blockers and proton pump inhibitors.
Diet. If it's bothersome, it may be prudent to re-evaluate your intake.