I would certainly take off the weeds from the manure. One of the most common is sometimes referred to as manure weed otherwise known as fat hen. It starts off small and looks very innocent when it is easily hoed off. But at a over a meter tall and producing up to 1/4 million seeds per plant it is a pain, and difficult to pull up. It best removed asap. The seeds stay in the soil for years, anytime anyone rotovates up they come to the surface and presumably will continue for more than seven years. This is our sixth year and there is still not shortage, when people rotavate for the sixth time.
It maybe worth raking the manure over to persuade more weeds to germinate before you spread it around.