The word you're looking for is magazine (from OED):

> **Magazine** *noun* 1. a paper covered, illustrated periodical containing articles or stories etc. by a number of writers.

You example fits this definition, since it has a paper cover, comes out periodically (weekly in this case), and has more than one writer.

Another possible word is anthology (from OED):

> **Anthology** *noun* a collection of passages from literature, especially poems.

Although the definition restricts the pieces in the collection to literature, so is less appropriate.  

If the works are later published all as one it could be called an "omnibus edition".