"I am busy until the weekend."
Someone correct me if I'm wrong: The subject isn't "weekend," but the implied "I." The full sentence would be 私は週まつまでいそがしいです。私 and such are dropped when they are already understood. It's like in English being asked "When are you busy?" and you reply "The weekend." instead of "I am busy during the weekend."
Well the Topic is "i" the subject Would be weekend (ga for marker) but since this is getting into a bit more complex grammar and structure, it uses different particles. Such as "made" instead of ga. The "made" lets you know that the weekend is almost doing something, where as "ga" just seems to show that it is just there.
The weekend isnt the topic or subject (2 different things just wanna point out that). we arent using "ga" because we arent making a statement about the weekend. Its a statement about you and your activity (busy). Time is always complicated in languages. If it helps the "maDe" is sort of acting like a marker, to say when your business ends.