either 주말마다, 매주말, or 매주 주말. also need 에서 particle since you are talking about "every weekend" as a time you do something rather than about the weekend itself, and the verb doesn't pertain to an action where you change location.
매 is not used in Korean in this way. Only as a prefix for something like 매일, but not 매주말.... Especially when - 마다 is used because it would imply the same meaning.
The notes for the lesson explain that this is for emphasis, much like "each and every" in English
As said below 매 is redundant and incorrect. Also if you choose We watch movie together every weekend it says you chose the incorrect answer :P, it may sound funny but it is still correct