Okay, so, there are two issues present here:
1) If your live tiles NEVER update, even after opening the apps, you might have the stuck app problem, usually caused by crashes or issues. Clear the IE history, & reset with vol down & power. Then wait. It may take a few times for this to catch, but it works, trust me.
2) This second issue is the one I just had. Its the same damn bug from WP7. Once you have x amount of apps with live tiles - whether they're enabled or not - the system can't update them. They'll update once after opening the app, & freeze again. This is solved by uninstalling apps listed in the background tasks part of settings. Amazing Weather may have just been coincidental. Chances are, any app would've fixed this.