Heat grill to medium heat.
Shape meat into 4 (1/2-inch-thick) patties. Brush onions with 2 Tbsp. dressing.
Grill patties and onions 5 min. on each side or until patties are done (160°F) and onions are tender, occasionally brushing onions with remaining 2 Tbsp. dressing and burgers with barbecue sauce. Top each burger with Singles; grill 1 to 2 min. or until Singles begin to melt.
Fill buns with lettuce, tomatoes, cheeseburgers and onions.