Island Air will increase fees on checked bags starting Tuesday for customers not enrolled in the airline’s Island Miles program. The new fees for nonmembers will be $25 for the first checked bag, $35 for the second and $35 for each additional checked bag. For Island Miles members, fees will be $15 for the first checked bag, $20 for the second and $35 for each additional checked bag. Island Air offers 238 flights each week between Oahu, Maui, Kauai and the Big Island. Founded in 1980 as Princeville…