According to my fairly inaccurate kitchen scales the old ones weigh about 10g, the new ones weigh about 25g. So it's about a 5.6x drop, which is still fantastic.
I think everyone talks about the number of bags as it makes the decrease look bigger.
Environmental organizations here actually complained about the plastic bag tax because they feared it would lead to people buying garbage bag rolls instead of reusing the grocery bags for their garbage.
Anecdotally I'd say it also makes our garbage system "less messy" than systems that depends on bigger thrash bags - a hole in a large flimsy thrash bag is more likely and has a bigger negative effect than one in a small sturdy one.
Charging for bags was commonplace in the UK in the 80's ... how long have you been keeping these for??
I now have loads of "bags for life" because sometimes you forget to bring one, don't bring enough or shop on a whim.