In an airtight container, combine the wings, pickle juice (including the pickles, if desired), and dill weed.
Seal tightly and refrigerate for at least 4 hours to marinate.
Remove the wings from the marinade and arrange them on a wire rack set over a baking sheet.
Pat them dry with paper towels, then return them to the refrigerator for about 1 hour.
Preheat your grill to 375°-400° and set it up for indirect heat.
Remove the wings from the refrigerator and season both sides evenly with Cajun seasoning.
Lightly spray the grill grates with nonstick spray, then arrange the wings without overcrowding.
Close the grill and cook for 20-25 minutes, or until the wings are golden in color, then flip.
While the wings continue cooking, prepare the sauce.
Place it in a grill-safe bowl and warm it on the grill for about 5 minutes, just until it begins to gently simmer.
Brush the wings with the sauce and continue cooking for an additional 15 minutes, or until they reach an internal temperature of 200°.
Remove from the grill and allow the wings to cool slightly before serving.