"A weak wind blows."
That sentence doesn't really make sense (from my knowledge). Wind is "かぜ", and it seems you broke apart the "か" and "ぜ". And "weak wind" is "よわい かぜ". The adjective goes right behind the word it is affecting. The sentence you were trying to make might be translated as "A wind blows weakly", as you are trying to modify the verb instead of the noun. Maybe "かぜはよわくふきます" would be what you were aiming to write. But no, it shouldn't be accepted (as far as my knowledge in this matter goes).