When you can't decide between two things, so you and another person (usually a friend or acquaintance) each purchase one of the desired items and you both exchange half of each item with one another.
Note: Most often done when ordering food. This way you can eat both items you want instead of ordering two meals and looking like a fat ass.
Person 1: "Man, I can't decide between the teriyaki chicken or the club."
Person 2: "Yeah, me neither."
Person 1: "Double halfsies?"
Person 2: "You read my mind."
This is when you use a high ball glass and pour half the cup full of vodka and then the rest add flavored mineral water. It is customary when this is done for first-timers to show the person so they see that half of their drink is vodka.
Bob: Yo, what are we drinking tonight?
Gerald: We sipping on a halfsee.