Reg Savvy will have a lot of theoretical information about how regulators work. To briefly answer your question, there is no direct relationship between balanced 2nd stages and venturi assist. "Balanced" means that the pneumatic forces on the valve in the 2nd stage don't change much with changes in supply pressure to the stage. I'm not sure how much you know, but the first stage sends air under pressure to the 2nd stage; that pressure is called intermediate pressure or IP. In almost all 2nd stages, the IP is pushing the 2nd stage valve open, which means you need something pushing back to keep the valve closed until you take a breath. Unbalanced 2nd stages use a mechanical spring to counter the force of the IP air. Balanced 2nds route some of that air into a chamber, which then allows it to push back against the air pushing from the 1st stage. This is helpful if the IP changes as the tank empties, for example. It's a little more complicated than this, but not much, really.
Venturi assist is present in essentially every 2nd stage to some degree or another, and it's adjustable in some 2nd stages. Basically it's caused by air moving quickly through the 2nd stage in a linear fashion; this creates a slight drop in pressure in the surrounding area, which then helps to keep the valve open and air flowing. It's the reason that many 2nd stages will keep flowing if you press the purge. Since all 2nd stages move air through a small valve relatively quickly, they all create some sort of venturi effect.
You might find the first chapter in the Vance Harlow book helpful too; it's a good explanation of the basic air forces at work in the common types of 1st and 2nd stages. You would also benefit from looking at some of the classic regulators with a mentor and take them apart to see how they work. It's amazing how simple some of the great scuba regulators are. If you can get your hands on a MK5 with a 109 2nd stage and go through the rebuilding process with an experienced tech, that would be very helpful, and enjoyable.