"Do you have time this weekend?"
The verb-not-verb structure (有没有) makes it a question. This is called affirmative-negative question. Instead you could just use the verb (here 有) and append 吗 to the sentence (你这个周末有时间吗？).
Affirmative-negative questions work with verbs and adjectives and usually take 不 for "no" (e.g. 你累不累？ Are you tired?), but the verb 有 requires 没 instead. See here for further explanations on affirmative-negative questions or here for an overview on questions in Chinese.