e.g. This thing has no calories, therefore I feel justified in overindulging and drinking tons of it to let my primal urge for sweetness go unopposed.
I realized a long time ago that I really enjoy drinking soda, and not much else. Very little interest in alcohol, sure I have some with friends but never when alone. Don't drink coffee (I have, of course, but never particularly enjoyed it or drank it regularly). I do enjoy Gatorade and fruit juice, of course it's because they are sweet.
Anyway, I also realized that if I'm going to drink soda regularly, I had to switch to diet. Just for the calories, really, at the time concerns about sugar weren't as prominent. But I gained a bit of weight in my late teens and switching to Diet Coke was a "free" reduction of 500 calories per day. "Free" as in, easy to switch, no dieting, no eating less, etc.
My point here is that I think the refill situation is the opposite of what you suggest -- diet soda doesn't cause me to drink more, it's the fact that I've always drank a lot of soda that caused me to choose diet soda.
Oh, and maybe it's related, I love chewing on ice that has been doused in soda. A server sees an "empty" glass and wants to clear it, but I see a mountain of delicious ice. Weird, I know.
7-11 started selling an enormous 128 oz mug that we would fill with soda in the morning and drink throughout the day. That was an insane amount of soda. But my boss at the time would have me take his 128 oz mug and fill it with several pots of coffee. The clerk at sev would joke about how she had to make a couple of extra pots around 8 am because of my boss, and how "I know it's still for him even if he's too chicken to come in himself."
To this day I've never known anybody that drank as much caffeine as he did. I'm guessing the nicotine from the chain smoking helped take some of the edge off :-D
Those were different times.