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1.
A meeting between two people that are not in a relationship together that occurs after 1:00 a.m. where there's not much talkin, mainly sex.
" Man I can't wait for my late night hype he's not my nigga just a late night hype, last time we didn't get together till 3:00 and the sex was somethin' serious"
by Missy Pooh September 28, 2005
 
2.
When you meet someone you're not dating or in a relationship with at a time after 1 a.m. You hang out, hook up, have sex, etc. It's a really fun thing to do.

Often mentioned in rap songs. Check out Compton's Most Wanted "Late Night Hype" (all parts 1-3).
I'm hooking up a late night hype with Alexandra at 2 o clock tonight. Last time I had one with Daniella I had a great time.

"Swooped to my girl house to see what was poppin
To let me know if the panties was droppin
Baby wanted snaps, twenties by the dozen
I guess the tramp thought that the E was buzzin
I couldn't fade it, why the hell should I jib?
Got the 20 sack of thai, and I'm here for the crib
I can't go out like that, that ain't my type
I hooked her up on my late night hype"

-Compton's Most Wanted "Late Night Hype Part 1"
by Bigfootbeleva13 July 24, 2009