Why can't you say
Dis-moi quetu fais le weekend.
Dis-moi ce que tu fais le weekend.
The 2nd sentence is grammatically correct. The question relates to the whole idea of 'WHAT you do on the weekend' and this requires 'ce que' (followed by the subject pronoun in this case). Que cannot be used (none of its translations fit to give a meaningful sentence).
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