The pre-trip ritual
Weigh each bag on the bathroom scale (you minus bag, or a hanging luggage scale), against the specific fare's limit. The ritual catches the overweight bag while redistribution is free — at home, moving shoes to a carry-on costs nothing; at the counter, it costs $100.
The counter negotiation, prepared
When the bag is over and carry-on space exists: move the densest items (shoes, books, chargers) and re-weigh. When it is not: the second-bag fee versus overweight fee comparison — usually the second bag wins below ~20 lb over. Both moves are arithmetic you can do calmly at home and execute in ninety seconds at the counter.
The return-trip trap
Souvenirs are dense and the return flight has different fees (international-origin fares sometimes differ). Re-weigh before the return leg — the hotel bathroom scale works — and ship the overflow mid-trip if the numbers say so. The overweight fee is always paid by someone who thought the way home was the same as the way there.