Of course the big cost for suppliers is that packaging itself costs money.
There are smart people with maths degrees who do stuff like work out whether it's cheaper to use less packaging, or allow more goods to get trashed in transit.
You can shift this equilibrium a bit, but not much without doing more harm than good. A depressing % of goods are thrown away (with their packaging) because they didn't make it to the consumer 100% intact.
If you tax packaging too much, then you increase waste through more damaged goods.
The "perfectly ripe" stuff in Waitrose simply wouldn't make it to the shops unless you packaged it more than bog standard spuds.
Not saying you shouldn't tax a bit, but Le Chatelier will get you if you try too hard. Henri-Louis' work can cause Greens to quite literally froth at the mouth.
As for "pretty, but useless" packaging, there is certainly room for reduction in waste here big time.
But...
For many goods like cosmetics the packaging is already a high % of the manufacturing cost, and they spend because it gets more sales.
As I recall cosmetics packaging is the second largest consumer of gold.
So I think small taxes would simply have no effect on their behaviour.
Big taxes get political, and they'd probably accept higher costs than reduce sales anyway.
Consumers can have a big effect here, as long as they are properly informed, rather than being driven by mindless Green/BBC propaganda.
In Germany, the "recycling" measures were loved by many local manufacturers, which confused the Greens in government, and even now they still haven't realise that it's simply a neat protectionist measure.