The Amazing Spider-Man 2 starts with a scene where Peter is shown falling down from a great height. He couldn't rise so high with his webs. How did he do that?
He's freefalling after launching himself at the top of a swing.
Clearly, as we see from later shots he has the ability to launch himself into the air (unsupported by webs) at the top of a swing much higher than the buildings around him that form anchor points for the webs.
As he reaches the top of the swing he just let's go of the web and continues upwards based on momentum until such time as gravity takes over again.