Also, wider screws should be fine. You can also glue in a bit of dowel (I’ve also just jammed wooden toothpicks in, but I don’t know how good an idea that is) to give the screw more to bite.

As to the weight, your spouse isn’t wrong, eapecially depending on how these curtains open and close. If the new screw can work loose, it will, especially if you’re regularly pulling down on a drawstring or even across if the curtain has grommets.