Whisk together the ketchup, water, white sugar, brown sugar, vinegar, mustard, salt, pepper, and paprika in a large saucepan. Bring to a simmer over medium-high heat; reduce heat to medium-low and simmer 15 minutes.
Meanwhile, heat a large skillet over medium-high heat; cook and stir the ground beef and onion in the hot skillet until the beef is crumbly, evenly browned, and no longer pink; drain and discard any excess grease. Stir the beef into the simmering barbeque sauce. Simmer together for 10 minutes. Spoon into the buns to serve.