Broilers vary in heat intensity; move the rack to a lower position if the chicken is browning too quickly, or to a higher rack if too slowly. Remove items from the baking sheet as done, if they're cooking unevenly.
Preheat broiler with rack 6 inches from heating element. Place sweet potatoes on a rimmed baking sheet and toss with 2 tablespoons oil; season with salt and pepper. Spread in a single layer and sprinkle with brown sugar. Wrap each cutlet with a bacon slice; tuck onion between bacon and chicken. Arrange alongside potatoes on sheet, onion side up; season with salt and pepper.
Broil until chicken is cooked through and potatoes are tender, 8 to 10 minutes. Toss watercress with remaining 1 tablespoon oil and vinegar, and season with salt and pepper. Divide chicken, potatoes, and watercress evenly among 4 plates and serve.