Your answer don't have to include the word "plans " or "weekend." There's no need to repeat every element of the question in your reply. I would suggest: I'm going to play basketball.

We need to say “my plans”, not just “plans”. Other than that, your sentence is grammatically correct either way, although it sounds better to use the infinitive in the predicate rather than the gerund. That said, the sentence is not very natural. More natural options would include: “I’m going to play basketball”, “I’m playing basketball”, or simply “Basketball”. (The one-word answer is not a sentence, but it works in casual conversation.)

I wouldn't say this weekend. I'd say, 'Do you have any plans for the weekend?' I would also say, 'I plan to play basketball or switch', 'I'm planning on playing basketball or switch.', or 'My plans are to play basketball or switch.'