Burping after eating and drinking is perfectly natural, as we consume quite a bit of air every time we swallow (via our noses), which avoids creating a "vacuum" by stabilizing air pressure inside our heads. Plug your nose and swallow, and you'll see what I mean: your ears will pop instead--the pressure release has to come from somewhere.
However, burping that persists between meals, or when your stomach is empty, means gas is coming from somewhere: stuff in your stomach seems the likely culprit, though I've heard of intra-abdominal pressure pushing gas backwards (also contributing to GERD) so you could be belching stuff from the upper portion of your small intestine. SIBO is a good thing to explore. Gases can also be released as stomach acid neutralizes and breaks down stuff in your stomach.
I had a history of GERD that I seem to have cured after going paleo, but it did take months. Low stomach acid persisted for quite awhile after stopping the PPI drugs I was taking, and low acid sure seems to have led to copious burping for hours after eating.
My first experiment would be to reduce eating frequency, so there are more periods where your stomach can empty fully. As long as there's food in there, you could have some gas production. Despite the old joke, "better to burp and taste it than to fart and waste it," if you burp and taste your last meal hours later, stuff is perhaps hanging around in there too long. I had some relief from taking Betaine HCL (a stomach acid replacement) and digestive enzymes--and also not drinking fluids with meals, which can perhaps dilute stomach acid so it takes longer to break stuff down. I would also avoid eating brothy/watery soups with other foods, for the same reason. Eating broths is great--but maybe not as a side along with lots of solid food, at least while you're trying to sort this out.
Another piece of advice is one your grandmother might have given: eat slowly, smaller bites, and chew your food thoroughly to mix in plenty of saliva, which itself aids in breaking down food. I've read that certain components in saliva also stimulate digestive enzyme production. Fast eating in large bites may encourage swallowing more air with your food.
I also notice my bodily posture while eating contributes. Slouching in a chair (like at one's desk at work), or wearing trousers with a snug waist, while seated bent at the waist, causes me more discomfort during/after eating. Sometimes if I'm feeling burby and refluxy, sitting up straight or standing up relieves pressure considerably.
Those are my thoughts, but naturally everyone's individual experience will vary. Others suggested changing the foods your eat, or the rations of each kind--all sound advice.
