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.
Now, you don't get given a bag for your Sandwich & Water at lunch, and you don't get a free bag with your McDonalds meal to name just a couple of services.
1p or 5p wouldn't make much of a difference? A Family paying 100 pound a week on shopping at a super market, can easily just spend 100.35 on 7 bags and won't bat an eye lid.
If that was 107.00 that would make a real difference and I bet the decrease would be much greater.
https://market.subwiki.org/wiki/Zero_price_effect
The same acts in reverse.
I personally reuse the same bag every time I go shopping until it is damaged. When I walk to my local, I carry the two or three items I bought directly, rather than in a bag. I could afford to buy over a million plastic bags a year, yet I've changed my behaviour to avoid buying them whenever possible.
(In my case, it has nothing to do with being asked, as I invariably use the automated checkout machines. Bags are available for purchase adjacent to these machines, so it's not an availability problem either.)