In 4-quart Dutch oven, heat 1 to 2 inches water to boiling. Add beans; boil uncovered 8 to 10 minutes or until crisp-tender. Drain; return to Dutch oven.
Meanwhile, in 10-inch skillet, melt butter over medium heat. Add shallots; cook 2 to 3 minutes, stirring occasionally, until crisp-tender. Stir in sugar. Cook 2 to 3 minutes longer, stirring occasionally, until shallots are glazed and brown. Stir in lemon juice, dill weed and salt.
Add shallot mixture to green beans; toss to coat.