In a saucepan over medium heat, combine blackberries, ketchup, brown sugar, apple cider vinegar, Worcestershire sauce, smoked paprika, garlic powder, onion powder, salt, and black pepper. Cook until the blackberries break down and the sauce thickens, about 10 minutes.

Preheat the grill to medium-high heat. Season the beef tenderloin with salt and black pepper.

Place the beef tenderloin on the grill and cook for about 20-25 minutes, turning occasionally, until it reaches an internal temperature of 135?F for medium-rare.

During the last 5 minutes of grilling, brush the blackberry BBQ sauce over the tenderloin.

Remove the beef from the grill and let it rest for 10 minutes before slicing. Serve with additional blackberry BBQ sauce on the side.