"Do you have time this weekend?"
Normally I'd be all for accepting the subject in front of time phrases as an alternate arrangement, but in this sentence it sounds rather awkward. You could omit the subject, though. Any second opinions, native speakers?
I agree WillowsofXihu, you could deffinatly omit 你 here: "这个周末有没有空" (as long as it's understood by the listener, I would probably be most likely to choose to say it that way.
Why not "这个周末你有时间吗" ? I can see no reason why the 有没有form must be used, and not the 有...吗 form.