Mix vinegar, water, sugar, 1 teaspoon salt, and 1/8 teaspoon pepper.
Cover; chill thoroughly.
Mix beef, 1 1/2 teaspoons salt, and 1/8 teaspoon pepper; shape into 16 patties.
Broil beef patties 3 inches from heat till done, about 8 minutes, turning once.
Place half the beef patties on bottom of buns.
Drain vegetable mixture; spoon some onto patties.
Top with remaining beef patties and more vegetables.
Add bun tops.