I can't say I agree that "You work little" is broken English, though "You don't work much" would surely be more common. I mean this in the context of English in general, not specifically in the context of this sentence.
But consider, for example, "I work little on the weekend" or (though a bit different) "On my new diet, I eat little on Tuesdays and Thursdays." I understand the contextual difference in these examples, but I am addressing your point that "work little" is "broken English."
With respect to the sentence, IMO it sounds weird because in English we are used to phrasing like "You X too much and Y too little" and vice versa. But that translation is not true to the Czech sentence given here, so I understand why the second "too" is omitted. VladaFu's comments a bit lower down further explains the rationale.
I truly thought it was fine but just weird, originally as well, so I get where you're coming from.
You're adding those objects though, "on the weekend" and "on Tuesday and Thursdays". Those objects are what's missing. I agree, those added, it's fine.
There's something else going on here that I can't put my finger on. I think it's something about 'little' being abnormal as an adverb. You could definitely use something with a -ly right? Like, "you work loudly". That's fine. Even "you work A little" would be better. Still weird though.
Here's dictionary.com usage, this doesn't fit any of them but it doesn't exclude it per se, admittedly.
adverb (usually preceded by a) in a small amount; to a small extent or degree; not a lotto laugh a little
(used preceding a verb) not at all, or hardly he little realized his fate
not much or often we go there very little now
little by little by small degrees
I think it's just not being processed as an adverb and in this usage is formed(for some reason, lack of the other verb, lack of the 'a', etc) as an adjective. So the sentence is like: "You work happy". Yeah, that's exactly what's happening. I don't know about you but I get the same feedback from "You work happy" as "You work little".
If I didn't convince you, that's fine. It was academically interesting to me and I'm happy with the line in the sand I suppose, we can agree to disagree. I'm sticking with calling it broken English though. You won't find any usage like this(I think I saw on google where you got your weekend example from, assuming you went looking!, ha ha).
This is not what's happening though. 'You work little' is not a complete sentence in English.
What's happening is that, if there's an 'and' we can often duplicate a condition from a prior statement and add it to infer a complete one. So what we try to do is add the 'too' and get the complete sentence, 'you work too little'.
This can't happen in this sentence though because it's 'work little' and we can't add the 'too' into the middle of 'work little' so It's just wrong and totally broken English.
From what you're saying, Vlad, It's not even being understood correctly. Because the english understanding includes the 'work too little'.
At first I thought this one was like similar awkward sentences in the tree that are technically correct English but this one just doesn't work.
To have a better translation I'm afraid we would have to say something like, 'you talk too much and work very little.
I googled "work little" and "you work little". I don't see it used in any kind of proper way.