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1.
Either "house" or "hook" in Ebonics depending on the way one uses the word
That was off the Heezie(hook)

Come to my Heezie(house)
by Phoenix Orion March 25, 2004
 
2.
it pretty much means any word that starts with H. most likely hook.
that shit is off the heezie fo sheezy my neezy, my nose is itchy i gotta sneezy
by spanky February 13, 2004
 
3.
house..see also beezie and fosheezie
let's go back to my heezie
by big johnny July 09, 2002
 
4.
To be 'off the heezie' is to be "radical" or "awesome"
Woah, this is off the Heezie
by Salami July 20, 2003