Cut each onion into 12 wedges. Cut bacon strips in half widthwise; wrap a piece of bacon around each onion wedge and secure with toothpicks. Place in an ungreased 13-by-9-inch dish.
In a small bowl, combine the brown sugar, vinegar, molasses and barbecue sauce; pour ½ cup over onions. Cover and refrigerate for 1 hour, turning once. Cover and refrigerate remaining marinade for basting.
Drain and discard marinade. Grill onions, covered, over medium heat for 10–15 minutes, turning and basting frequently with reserved marinade.