Yes, indeed, this comprehensive body of law gets bigger everyday - but the peoples of Europe have only the very vaguest of influence upon its formation. There is no European-wide political process that could possibly reflect upon the acquis communitaire, which emerges instead as a huckstering between national elites.
It is socially illiberal, patrician, security-driven and for the last quarter century dominated by the lowest-common denominator of market liberalisation.
For the newer states that joined in 2004, legislatures were expected to vote the entire body of legislation built up since 1958 onto their statute books in a single act - not surprisingly the possibility of any scrutiny of 46 years of legislation in a single parliamentary sitting was perfunctory.
I don't say that the US equivalent is necessarily any better, but I can say with confidence that almost all Europeans look on EU law as opaque and unresponsive to their will. We call it the democratic deficit.