o certo é dizer "I hope she have a great weekend" invés de "I hope she has a great weekend".
Por quê nao poderia ser "I hope it not rain" ou algo parecido? No segundo caso, a ação ainda não aconteceu, assim como no primeiro, então por quê usamos o simple present?

     I think something gone amiss here, or you was misled by some reasoning.

     In fact the DOES in "I hope it does not rain" is because you need it to make questions and negative sentences.   And, as you are talking about "it" (phenomenon of Nature), hence goes with DOES third person singular in such a sentence.

   Thus, the NOT, generally asks the presence of the DOES.

   This way, when you come up with a phrase like "I hope it not rain" you can bet that

it requires a DOES before the particle not  "I hope it does not rain", in other words, NOT in itself don´t suffice to negativate the expression at all. 

   When in the sentence "I hope she have a great weekend" the negative way would be:

"I hope she doesn´t have a great weekend."

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    Quanto ao "I hope she have a great weekend" invés de "I hope she has a great weekend".  Isso eu não sei agora, só sei que foi assim! 

    E é assim...