It seems that your English is good enough that you'd benefit from an English/English dictionary instead of relying on a German/English dictionary. That way, you're understanding the meaning in the same context as native speakers and without being tainted by connotations of words used in the German definition. (I have this problem all the time with English/Japanese dictionaries; I look something up and it doesn't make sense. Then I look it up in a Japanese/Japanese dictionary and everything makes perfect sense. Of course, sometimes that requires a few more trips to the dictionary to understand the definition, but...)
Anyway, if I were learning English I'd pay the $300 for an Oxford English Dictionary. You'll learn a lot that way.
I will explain it once again and in full and then let it go.
This is a special case. I know that normally barely meanst "only just" (though i believed leo that it sometimes - in special cases when used in a specific way - can mean "only almost"). But if someone hears a sentence like "that is barely visible", one always implies that it is not visible at all for someone seeing a degree worse. Now, if you vist a pornsite with usergenerated content - take 4chan as example - I'd bet a lot of money that one would find a mod-guideline or at least a discussion about such a guideline to delete any threads with "barely legal teens" as topic because a lot of users would post pictures of underage girls in such a thread. In such a case, barely implies not really. And therefore such a term can have another connotation than its formal meaning.
It is really a stretch to say "it doesn't have that connotation", connotations can vary even in one language for every speaker.