Again, I don't live in the EU, so it has not influenced my life in the slightest.
I'd refer to it as heavy handed because of the regulatory burdens it imposes upon its member countries. It represents a super-government enacting laws and regulations that impact every citizen of the member country's with only an indirect accountability to the electorate.
Here is an instance of the EU going after Google:
http://www.theverge.com/2016/4/25/11490452/why-eu-antitrust-...
Whatever you think of this particular action, this is a broad power, imposed on behalf of all the members states. Similarly with the 'right to be forgotten' law. The power to implement these kinds of things is, in my view, 'heavy-handed' and overbroad if your goal is simply to facilitate free movement of people and goods. Why is the EU telling Google it has to forget people?
The reason, in my view, is that power naturally moves up the stack when there is another place for it to move up to. So, because the EU sits on top of its member nations, it will gradually acquire more and more power over time. This is not inherently good or bad, of course. It's just the way the world works. But it can be bad if that organization is insufficiently transparent and democratic, and it also can be bad if there is an economic heterogeneity to the composing countries.
This is particularly evident with the Euro (which I realize the UK does not use), but it can be true with other economic policies. But in the case of the Euro, you have countries like Greece that vastly overspent and totally screwed themselves with debt because of the cheap credit the Euro allowed them. Ordinarily in a situation like that, the offending country would simply print more of its own money, causing inflation and pain for its population - which would then shift the political discourse of that country toward fixing the inflation - achievable primarily through genuine economic reforms. But in Greece this didn't happen and doesn't seem likely to, and this is, in my view, because they don't control the currency. They can't inflate away their debts, so they are stuck, and the people of Greece blame the EU and the EU blames the people of Greece. But the truth is that they're both right - the structure of the EU prevents Greece from fixing the problem itself - but of course Greece is responsible for creating it in the first place.
Now, I realize the above is not the same as the UK and that the UK does not use the Euro. That is just a convenient example of what kinds of problems are entailed by having a sort of shadow economic government over and above the regular one. That there is a sort of impedance mismatch that precludes natural economic realignment because power is split up in an awkward and nonsensical way that promotes the interests of the larger body over the interests of its member entities, but does so in an incomplete, indirect way.
I guess what I am saying is that if you want a unified Europe you should have an actually unified Europe under a single government. But having this pseudo-government in charge of economic things and some other stuff, but then not other things will end up creating these barriers to natural economic fluctuations that will ultimately harm the entire continent.