The first instinct of many Weber charcoal-grill users is tossing meat on the cooking grate directly above the coals and charring it until it is done. Thick, long cuts of whole pork tenderloin, however, require more care and patience before and during the grilling process. The kettle shape of Weber grills is perfectly suited for the slower cooking method of indirect grilling, in which the lit coals rest on the sides of the grill and the loin sits over a coal-free zone in the center of the kettle.
Curing the Loin
Mix the brown sugar and dry seasonings in a small plastic bowl, breaking up any clumps with a fork until everything is thoroughly blended. This forms a dry-rub seasoning.
Place the tenderloin atop the metal baking sheet, and coat the meat with the dry-rub seasoning, rubbing the spices over all the meat's surface with your hands.
Cover the tenderloin with plastic wrap, tucking the edges underneath the baking sheet to form a tight seal. Refrigerate the covered tenderloin overnight, letting the dry-rub soak into the meat. This cures it, creating a protective moisture barrier for the fiery cooking process.
Grilling the Loin
Toss the wood chips in the small plastic bowl and fill the container with water until chips either float or submerge. Soak them for at least an hour prior to starting the charcoal fire.
Open the top and bottom grill vents. Remove and hang the lid on the side of the grill using the built-in lid hood, and remove and set aside the cooking grate.
Fill the top compartment of the charcoal chimney starter with natural lump charcoal and crumple the newspaper into the starter's lower chamber. Place the starter inside the grill on the center of the Weber coal grate and light the newspaper from below.
Wait at least 20 minutes until the coals glow or take on a gray hue. Lift the chimney starter from the grill using the protective handle and place the Weber charcoal baskets on either side of the grill, leaving a coal-free zone in the center of the coal grate. Dump a roughly equal portion of lit coals into each basket and place the foil roasting pan between the baskets.
Pour the cooking sherry into the foil pan. The sherry heats up and releases meat-flavoring vapors during the grilling process. It also extinguishes hot grease drippings, preventing flare-ups.
Place the cooking grate back into the grill so that the hinged grate flaps rest directly above and are aligned with the charcoal-cooking baskets.
Fold the paper towel into a small square and saturate it in vegetable oil. Grasp the square with long-handled grilling tongs, and drag it over the center portion of the cooking grate, lubricating the cooking surface.
Place the cured loin atop the cooking grate directly above the foil-roasting pan. Ensure that no portions of the meat rests directly above any lit coals. Open the hinged cooking-grate flaps, and toss an equal amount of wet wood chips on each pile of lit coals. Close the grate flaps and close the grill lid. Position the open lid vents so that they rest downwind and between the two charcoal baskets, as this draws smoke and heat evenly over the loin.
Cook the meat for 45 minutes to an hour -- depending on outside temperatures and wind speed -- ensuring that the meat reaches an internal temperature of 185 degrees Fahrenheit before removing the roast, and slicing and serving it.