powderman: 'Buckeyes' are Horse Chestnuts, at least in Ohio the Buckeye State, I believe. There are a number of different varieties of Chestnut, the Oak Chestnut and Horse Chestnut are not edible, I believe. The American Chestnut, the edible one, mostly died off between 1900 and 1904. There is some resurgence of the American Chestnut but it remains subject to blight. Some hybridization with European or Chinese varieties has been attempted. The most prevalent chestnuts are the Chinese varieties either grown in the US or imported. Most of what you would find in the market around holiday time is the Chinese Chestnut.
The nuts you describe sound just exactly like Chinese Chestnuts, flat on one side and rounded on the other, dark brown and delicious. The size on some may be due to the drought conditions.