No - hand over the credit card and say it's okay to pay the extra charge. If you're only a bit over, they'll probably let it slide "just this once" just because they don't want to do to the paperwork. That's what happened to me at NRT once.

And if they do in fact take you up on your offer to pay the overweight baggage fee, keep in mind that if you are actually overweight, then you actually do owe the fee and don't be too bitter about it.