In an email, such "premature" weekend well-wishing would be fine. In fact, you might say that it sort of sends an implicit message, something along the lines of:
(a) I'm not sure if we'll communicate again before the end of the business day, or
(b) I realize you may not read this message until this afternoon.
In other words, I might be less likely to close a Friday morning email that way with my secretary or boss (who I normally see every couple hours through the course of the day), and more likely to do so in an email to that IT assistant who works on the other side of building (who I may not talk with again until Monday or Tuesday next week).
But no, nothing “weird” about it – not in the U.S., either.