The three examples in the question are clear and natural enough that there is not good reason, I think, to take exception to them. A shorter form, possibly more natural, is “What's the weather this weekend?”
True, the form suggested by user3169 adds some precision to the question by acknowledging that a prediction or forecast is what is being asked about. But I think it unnecessary to insist upon spelling that out.
Regarding the tense, present tense rather than a future form is suitable because a question like “What's the weather this weekend?” will be understood to mean “What's the current prediction for what the weather will be like this weekend?” or to mean “What do you think the weather will be like this weekend?”.