One factor that I've noticed is that Americans love ice much more than Europeans. It's not uncommon for them to fill a cup with ice almost to the rim and then add the soda. It would be interesting to see how much actual soda most people put in those 1+ litre ups.
Ah, sorry. If you're talking about bottles, then yeah, 1~3 litres are normal here too. Single servings are either a can (330ml) or a small bottle (~500ml).
Unfortunately it's not a bottle. It's just a plastic cup with a lid and a straw. A really big plastic cup that tapers at the bottom so you can fit it in your vehicle's cupholder.