You know that annoying yowling cats make while in heat? Well, "Heeeyyyy" is the verbal expression that girls (or guys) would use to broadcast their instinctual urges.
1. (girl to girl) "Heeyy girrl!" ""Yea, what's up?"
2. (hot chick to guy) "Heeyy..." "Hi! U look kinda hawt"
3. (gay guy to gay guy) "Heeyy!! What to make out?" "Yeeaa, lets..."
Like other forms of the word "hey", this one is inherently sexual. "Heeyyy" implies that therecipient should tie themself to the bed and await the sender's arrival.