I only voted for a billion because I'm just too damn hopeful as a Spider-Man fan. My real prediction would be $800-850 million or maybe, just maybe $900 million.
My reasons (a lot of which were already mentioned):
1. Origin Story, Be Gone - A main problem people had with the first film was that it was doing the origin again, so naturally they skipped over it (and that it was a rehash, which is a very stupid remark against the first film).
Now this film has more of a chance because the main chunk of the origin is done, so this could get more attention than the first, which leads me to my next choice..
2. Star Power - The Amazing Spider-Man, to me, felt like an indie film that you'd see at a film festival, probably because of the cast. With this film, there's a lot more star-studded actors in this (Jamie Foxx, Paul Giamatti, Chris Cooper, etc.) while keeping the indy element from the first film. Again, this gives the sequel more attention from the GA.
3. Release Date - Spidey got squished last year, mostly due to the behemoths known as The Avengers and The Dark Knight Rises being people's most anticipated comic book movie. Luckily though, it was still a box office success so I digress. At least this time around, the competition isn't too crazy so it has more of a chance to garner some $$.
4. Sam Raimi, Be Gone - The GA loved Sam Raimi's Spider-Man, and a lot of them were not in favor of that franchise being rebooted, so it was just another mark on the first film. It's now 11 years since Spider-Man hit the big screen, 9 years since Spider-Man 2 and 6 years since Spider-Man 3 - Case in point, I think it's time to get over the fact that Raimi's series is long dead.
With that in mind, this could be the best opportunity for the sequel.