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1. I'm having a party (determiner) next weekend. (Isn't weekend countable? How come I don't need a determiner like 'a/the' ?) 2. I'm having a party the next weekend. (Is 'the' omitted in #1?)
1. I'm having a party (determiner) next weekend. (Isn't weekend countable? How come I don't need a determiner like 'a/the' ?) 2. I'm having a party the next weekend. (Is 'the' omitted in #1?)
"next weekend" is specific enough as is. There's no need to add "the" unless you intent to add something more specific. For example,
I'm having a party (not this weekend but) the next weekend.
Weekend 
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