American Airlines said last week that it will start charging $15 to most passengers to check a first bag, and that it plans to cut its schedule by as much as 12 percent. American also said it would raise other fees from $5 to $50 for a range of services from reservation help to oversized bags. This comes just a month after American joined other big carriers in charging $25 for a second checked bag. This means that if you arrive with two bags, the tab will be $40 each way. The fees will kick in for flights booked starting June 15. But it won't affect some American frequent-flier program members or those paying full fare or international passengers. American put the details on its website, aa.com. Delta reacted almost immediately, saying it was not planning to adopt the first-bag fee, but United said it would consider it.