Some Departure Control systems will have a built-in tolerance of X kilos and won't let the check-in agent proceed without a corresponding xbag payment.
Some airlines will have a performance penalty clause in their handling agent's contract.
Some check-in agents might be in a good mood. Others might not. Some mightn't like the colour of your tie.
You (or better - your wife) are at an informational disadvantage.
On the other hand, assuming that your wife's right ( they usually are...), I'd keep my bag at precisely 23kg and let her turn up with whatever she's convinced she can get away with, having told her at the outset that you don't necessarily agree (for the above reasons) , but it's her decision.
It'll be your fault anyway....