I think the point is proportional representation. For instance, as a Lib Dem or Green voter living in a constituency with a strong Labour or Tory majority, you are not represented in the UK parliament at all.

Being able to influence EU decisions through the EU parliament, which uses a more proportional voting system, at least gives you some democratic representation and accountability.

Besides, "overlay" is not quite the right word for the relationship between the EU and the national level. The term used in Article 5 of the EU Treaty is subsidiarity, which essentially means to handle things as locally as possible and as globally as necessary to solve the problem. So it's not like the EU gets to overrule national parliaments on anything and everything.

Of course you can endlessly debate what's possible and necessary in each individual case. But that's unavoidable. They're having the exact same debate in the US and the proponents of Scottish independence have yet another take on it.