Fill a large bowl with ice and cold water. Place potatoes in a large pot and cover with water; bring to a boil over high heat. Reduce heat to medium-low, cover, and cook until tender but still firm, about 15 minutes. Drain and immediately immerse in ice water until cold, about 5 minutes. Cut into bite-size pieces, leaving skins on, and place in a large bowl.

Combine mayonnaise, sour cream, green onions, and dill weed in a bowl until blended; season with salt and black pepper. Pour mayonnaise mixture over potatoes; toss to evenly coat. Taste; adjust seasoning if necessary. Cover the bowl; refrigerate 2 hours to overnight.