Checking a bag has gotten more expensive across the board, as airlines are increasing their fees due to rising fuel costs amid the war with Iran. In recent months, American , Alaska , Delta , JetBlue , Southwest and United have all announced price hikes of about $10 more per bag, with most checked luggage fees for domestic flights now starting at $45 for the first bag. With summer travel approaching, travelers could feel that financial pain — but there are solutions to avoid hurting their wallets. Checking a bag is more expensive these days, but there are ways to pack smarter to avoid a checked baggage fee. rh2010 – stock.adobe.com Paul Stewart, founder of shipping company My Baggage , told The Post that the answer isn’t a bigger carry-on bag — it’s packing smarter with the one you already have on hand. “Most people assume they can’t fit a week’s worth of clothes in a carry-on, so they default to checking a bag without even trying,” he explained.…