We introduced similar laws here in Portugal last year and my anedoctal observation is that most people buy the thicker bags at 10-20 cents. It is also very obvious that many items that used to be sold loose are now packaged or bring their own plastic or paper bag. I'm looking forward to the statistics next year.

EDIT: It is not clear above, I mean that most people don't reuse the bags, they just buy new ones each time.