I haven't seen Amazing Spiderman 2 yet... but this one is gonna have a hard time making a real profit.
http://www.comicbookmovie.com/fansites/JoshWildingNewsAndReviews/news/?a=99336#3muVFOv0aFzIiSKr.99Sony are apparently quite anxious to see how well the sequel performs, especially with a long running time and a whopping budget of $225 million (as well as around $190 million spent on marketing)
You figure with $0.50 on the dollar made at US theaters, and $415M spent on the movie and it's advertising (which practically showed the entire movie already).... to just make $415M domestic BO doesn't even come close to making it's money back. And for reference, the first Amazing SM made $262M domestic
It has 2 weeks till Godzilla and 2 more weeks after that till X-Men DoFP
China is expecting a large intake of BO, but US companies only get something like $0.25 on the dollar made, so they see even less back from Chinese theaters. I think Sony may have over extended themselves on this one... which wouldn't be good news for them since they already have a 3 more sequels in the works and the company as a whole is in the red. Spiderman is one of the few shining lights for Sony Pictures (James Bond being another tent pole), so seeing their "guaranteed" money maker, not make money by the truck load could be a problem.