Translation:Do you have time this weekend?
"Do you've time this weekend" is very unnatural. In English we don't elide 'you' and 'have' in this context. "Do you have time this weekend?" is a better translation.
Also. "Are you free this weekend?" should be accepted.
Actually, "Are you free?" is best translated as "你有空嗎?" (Ni you kong ma?) I also think that's the most natural way in Chinese to ask if someone has time! Perhaps a Chinese speaker can tell us whether "有時間" is idiomatic in Chinese or is it a too literal translation from English?
这个周末你有没有空？is okay too. But usually we don't say 有空 for work hours. 有空 means 有 空闲的 时间 (have free time / leisure time). 空闲 is pronounced kòng xián, not kōng xián.
Free time implies leisure time, what if you are asking a mechanic to look at your car this weekend?
Yes, 时间 = time whereas 空(闲) = free time. 空 literally means "empty / space / air"