I agree with the extra bag idea, but with a twist. I always make sure mine is stored in outside pocket of my carry-on suitcase. If I'm checking in luggage, and over the weight limit, I can grab it quickly and pull a few heavy things out of my suitcase and throw them in the extra bag. (shoes, books, laundry, jeans are usually the weight offenders). This embarrassing thing has only happened once, but I'll always be prepared.
My extra bag is an old duffel with no pockets, just one roomy compartment and a zip. We never used it because it's not a nice, structured, quality duffel. It was just a freebie many years ago. But because it has no features or shape, it folds as tiny as a 3x5 card.
Now airlines are starting to charge for a 2nd bag, this large shapeless bag comes in handy, cuz you can put the bag you had planned to carry-on into it, or it into your carry-on. And shapeless means it can be squeezed into small leftover overhead space, or made to be a foot pillow for you.
Traveling is all about flexibility: if the airline says your overweight, but doesn't charge for a 2nd bag, split your stuff up and check this as a 2nd bag. (or your travelling partner's 2nd bag!) If the airline says they'll charge you for a 2nd bag, it can be your big carry-on.
Many people don't realize that the carry-on rules for most American carriers is TWO bags. They say ONE carry-on, but that means one carry-on small suitcase. AND each person gets a "personal bag" like a ladies purse or a mens briefcase. Ladies choose a large tote that is malleable to maximize this.
Also small food bags don't count since the airlines changed the food service.