Using fork, crush 1 cup raspberries with 2 tablespoons sugar in small bowl. Let stand at room temperature 1 hour. Toss peaches with 4 tablespoons sugar in large bowl. Let stand at room temperature 30 minutes, tossing occasionally.
Press raspberry-sugar mixture through fine strainer set over bowl. Add 2 cups raspberries to strained puree; toss. Stir raspberry mixture into peaches. (Can be made 2 hours ahead. Cover and chill.)
