I think that "You should worry" meaning is to be "It is good for you to do worry", But in dictionary defines "You should worry" meaning is "You don't worry". How is the meaning to be "You don't worry"? I've been thinking it seems an irony sentence.
I think it might be helpful to think of the dictionary's definition as:
You don't worry enough.
"You should worry" would be said in only two contexts in English.
The speaker is confirming/adding new information, or
The speaker is contradicting.
The speaker will be Person A and the listener will be Person B.
In context 1, Person B is already worried about something. Person A states, "You should be worried", meaning that he agrees with Person B.
In context 2, Person B is not worried about something. Person A states, "You should be worried", meaning that he believes Person B is wrong and not worrying enough.
As an aside, English has a verb "to mean" that would make your sentence sound more your question more natural sounding.
I think that, "You should worry" means "It is good for you to worry"...
As you found it, it's totally irony. In a normal sense, that means that you absolutely have a reason to worry.
I don't think I have ever heard a person say "you should worry" to someone who he thought was not worrying enough. It would be more like "if I were you (or in your shoes etc), I'd be worried".
However the ironic version is much more common. Person A thinks that person B is worrying for no (according to person A) good reason... and in particular that some other person C (or A!) has much more reason to worry. In this case the emphasis is on the first word: "YOU should worry!". i.e. you do not have a lot to worry about... but person C has!
"You should worry" is not in any way ironic. It means "You don't appear worried enough about (situation), there is real reason to be concerned."