Sprinkle pork with 1/4 teaspoon salt and pepper. Oil the grill rack (see Tip). Grill the pork, turning occasionally, for 10 minutes. Brush the pork with 2 tablespoons preserves and continue grilling until an instant-read thermometer inserted into the thickest part registers 145°F, 2 to 5 minutes more. Grill apricot (or nectarine) halves on the coolest part of the grill, turning occasionally, until tender and marked, about 4 minutes. Transfer the pork and apricots to a clean cutting board and let rest for 5 minutes.
Meanwhile, whisk the remaining 1 tablespoon preserves, vinegar, shallot, oil, 1/4 teaspoon salt and pepper to taste in a large bowl. Cut the fruit into wedges and add to the dressing along with watercress (or arugula); toss to coat. Thinly slice the pork. Serve the salad with the sliced pork.