Combine the cherry tomatoes in a medium bowl with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add the sugar, lemon juice, vinegar and 1 tablespoon of the olive oil. Marinate at room temperature for a minimum of 30 minutes and up to 3 hours.
If the marinated cherry tomatoes have released a lot of juice, pour a little off before adding the remaining 3 tablespoons olive oil.
Place the arugula in a salad bowl and season lightly with salt and pepper. Add the cherry tomato mixture and toss to combine. Top with the parmesan. Serve.