The phrase “Wish you a happy weekend” would only be correct with the addition of a subject to accompany the transitive verb “wish.”
For example, we could say “I wish you a happy weekend.” This would be grammatically correct, although it would sound a bit formal.
If we left off the subject and just started with the verb “wish”, we would technically be creating a command. All commands come with the understood subject of “you”. If we added that understood subject to the phrase, we can see just how silly it sounds and the further grammar error it creates.
“(You) wish you a happy weekend.”
With the subject doing the action to the subject, we now have a reflexive verb. As such, the pronoun that follows must be the reflexive one (yourself). While you could command someone to wish himself a happy weekend, it would be rare.
On the other hand, the phrase “Wishing you a happy weekend.” can be used quite satisfactorily as a closing statement in an informal letter. Rather than signing off with “Sincerely” or “Regards”, you might precede your signature with this phrase.
This conveys a shorthand version of the phrase “I am wishing you a happy weekend.” A similar situation can be seen in the phrase “Looking forward to seeing you.”
With all that said, the combination of the words “happy” and “weekend” is a bit odd. In the U.S., we tend to say “a nice, good or great weekend” instead.
Have a great weekend!
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