Here are some nut studies that link to benefits in connection with diabetes, heart disease, and inflammation. However, it should be noted that they are often very small, and usually funded by nut organizations. I wouldn't put too much weight on such.
Nuts linked to improved type 2 diabetes health
A 3-month study involving 117 older adults (mean age 62) with diabetes found that 75g of nuts (½ a cup) a day, as a replacement for carbohydrate foods, can improve glycemic control and blood lipids in those with type 2 diabetes.
The nuts used were a mixed lot of tree nuts (almonds, Brazils, cashews, hazelnuts, pecans, pine nuts, pistachios, macadamias and walnuts) and peanuts. improved blood lipid levels and blood sugar levels in individuals with non-insulin dependent diabetes.
Jenkins, D.J.A., C.W.C. Kendall, B. Lamarche, M.S. Banach, K. Srichaikul, E. Vidgen, S. Mitchell, T. Parker, S. Nishi, B. Bashyam, R. de Souza, C. Ireland, S.C. Pichika, J. Beyene, J.L. Sievenpiper, R.G. Josse, 2018. Nuts as a replacement for carbohydrates in the diabetic diet: a reanalysis of a randomised controlled trial. Diabetologia https://doi.org/10.1007/s00125-018-4628-9
Eating pecans had significant effect on biomarkers of heart disease and type 2 diabetes
A very small 4-week study involving 26 overweight and obese adults (average age 59) found that those given a diet with pecans substituted for 15% of the total calories significantly improved insulin sensitivity and had a significant effect on markers of cardiometabolic disease.
Both the control diet and the pecan-rich diet were low in fruits, vegetables and fiber.
The study entitled "A Pecan-Rich Diet Improves Cardiometabolic Risk Factors in Overweight and Obese Adults: A Randomized Controlled Trial" is available online and was presented at the American Society for Nutrition Annual Conference, Nutrition 2018 held in Boston in June.
A handful of nuts a day cuts the risk of a wide range of diseases
A review of 29 studies involving some 819,000 participants has concluded that people who eat at least 20g of nuts (a handful) a day have a 30% lower risk of heart disease, as well as lower risks of cancer, respiratory disease, and diabetes.
The study included all kinds of tree nuts, and also peanuts. The results were in general similar. There was little evidence of further improvement in health outcomes as a result of eating more than 20g of nuts.
Nuts and peanuts are high in fibre, magnesium, and polyunsaturated fats. Some nuts, particularly walnuts and pecan nuts are also high in antioxidants.
(2018). A Pecan-Rich Diet Improves Cardiometabolic Risk Factors in Overweight and Obese Adults: A Randomized Controlled Trial.
Nutrients. 10(3), 339.
Link between nut intake and inflammatory biomarkers
Data from 5,013 men and women participating in the Nurses' Health Study and Health Professionals Follow-up Study has revealed that higher nut intake (5 or more times per week) was associated with lower levels of inflammatory biomarkers (C-reactive protein (CRP) and Interleukin 6 (IL6)).
Research has also shown that nut consumption may be inversely related to body mass index (BMI), which is a strong determinant of inflammatory biomarkers, so it may be that the associations between nut intake and inflammatory markers are mediated in part through BMI.
(2016). Associations between nut consumption and inflammatory biomarkers.
The American Journal of Clinical Nutrition. 104(3), 722 - 728.