“I eat so little, but still I feel heavy. Is there a problem with my digestive system?”

Maybe, but the symptoms are a bit vague and thus it's tough to make any conclusions with so little information. Bloating is usually due to carbohydrate malabsorption so you might consider reducing carbs in your diet. This usually help reduce bloating. A visit to your primary care doctor or a GI doctor will help make sure nothing else is going on.

This condition could be the benign functional bloating and frequently related to diet such as a high-fiber diet. However, before making this conclusion, I suggest you check some routine blood work for H.pylori and CBC and CRP and electrolytes. If there is any abnormality or if you have alarming symptoms such as vomiting or weight loss or diarrhea or GI bleed, you need to have further investigations with scopes. Things that work for functional bloating is low-fiber and OTC align probiotic or gas X, etc.

It maybe your diet, the types of food you eat, or it may be sign of a gastrointestinal issue. Please check with your doctor.