When the Weezers make it to Mt. Incredibly Unstable, they do a cheer similar to Rocky's cheer after he climbed up the stairs leading to the Philadelphia Museum with similar background music.
Carl puts on his glasses and realizes he doesn't need them anymore when everything is blur with them on. The same way it went for Peter Parker. He also climbs up a building and jumps from one building to another the same way Spiderman did.