In a bowl, whisk together the balsamic, lemon juice, and olive oil. Taste for seasoning. Set aside.
Place the tomatoes on a flat surface. Cut the smaller ones in half and the larger ones into slices. Arrange all of them in a single layer, flesh side up. Season them with salt, black pepper and sugar. Drizzle the tomatoes with the dressing. Toss them with the tarragon and strawberries.
Arrange the tomatoes down the length of 6 rectangular plates. Drizzle with the remaining dressing and top with the watermelon. Serve immediately.
Recipe courtesy Alex Guarnaschelli