Too much packaging

Can you see the over wrapping on this chicken
that I bought? It is vacuum packed, then
cling-wrapped into a styrofoam tray.

Japanese packaging often seems to be overdone. If you buy a packet of biscuits, chances are that when you open them you'll find the biscuits in separate packets inside the outside wrapper. We don't buy many of those kinds of packets, but still we seem to throw away an awful lot of plastic rubbish each week.

The plastic (pura) rubbish is separate from the wet/dirty rubbish like food scraps, so it gives you hope that they are recycling it. See this post for the symbol that tells you if plastic belongs in the "plastic rubbish", note that this is a different category to PET bottles. 

I really don't know what they do with the large amounts of plastic wrapping rubbish people throw out each week.

It's not just that they overwrap, the portions are small. Our family
goes through two of these frozen veggie packets a night.  

However, according to this article, Japan is one of the best plastic recyclers in the world:

This is about as large as the yoghurt comes in Japan: 400g. 

At 77%, Japan's plastic recycling rate is about twice that of the UK, and well above the 20% figure for the US, which still depends largely on landfill, according to institute spokesman Takushi Kamiya. One major driver has been the lack of space for landfill close to crowded and sprawling metropolitan areas.

This took less than a week to accumulate:
our plastic recycling rubbish.

But the same article does admit this:

Japan's plastic recycling operation would be easier if manufacturers reduced the amount of wrapping they use, said Kevin Carroll, representative director of EA International, an environmental and engineering risk management consultancy in Tokyo. 

"Japan differs from other countries in that it tends to overwrap," Carroll said. "You buy a bento boxed lunch and it comes in a plastic box with a lid, and then it's put into a plastic bag. Lots of other foodstuffs are the same. (My bolding.)