Anchorage School District officials are proposing to erase more than 500 staff positions, increase class sizes, eliminate many sports and make other cutbacks to close a massive budget gap next school year. “We’re laying off dozens of employees in departments across the district,” Superintendent Jharrett Bryantt said in an interview Monday. “We’ll be the leanest that we’ve been in over 15 years, and probably even leaner than that, and we still were forced to increase class sizes by four.”