Premium quality. Omega-3: 2.5 g per serving. The omega-3 in walnuts can help you get the proper balance of fatty acids your body needs for promoting and maintaining heart health. In fact, according to the Food and Drug Administration, supportive out not conclusive research shows that eating 1.5 oz of walnuts per day, as part of a low saturated fat and low cholesterol diet, and not resulting in increased caloric intake, may reduce the risk of coronary heart disease.