In a small saucepan, combine ketchup, brown sugar, vinegar, mustard, and Worcestershire sauce. Bring to a boil; reduce heat and simmer, stirring occasionally, until sauce thickens, about 10 minutes.
Pour sauce into a large bowl and set aside.
Crumble the chuck and sirloin into a bowl, sprinkle with salt and pepper, and toss lightly to combine. Shape into 8 (3 inch) burgers, about 1/2-inch thick.
Preheat grill to medium-hot and oil grill rack. Grill onions about 5 minutes on each side, or until softened and browned. Transfer onions to bowl with sauce; toss to combine.
Grill burgers, 3 to 4 minutes per side for medium-rare. Top with cheese during the last 1 to 2 minutes of cooking time, with grill covered, to melt cheese. Remove burgers from grill.
Grill buns cut sides down until toasted.
To assemble burgers, top bottom halves of buns with lettuce, tomato slices, and burgers. Spoon on onions, and top each burger with 2 pieces bacon and bun tops.