I had a similar problem last week when updating the latest Facebook Beta; it suddenly started draining 15% per hour. In fact, the charging could barely keep up with the battery drain. I have a Google Mail configured to sync every hour but it's not my primary e-mail and gets very little e-mail; I only use it for some things I don't want to give my Microsoft Exchange e-mail address to, which is set to sync as items arrive.
Anyway, I have Amazing Weather HD installed as well, and I have live tiles for WPCentral , Engadget, and Battery Performance.
I don't think that syncing Google Mail every 30 minutes is the culprit, but would it be possible for you to remove the account and add it back again to see if it helps?
What I did to fix my problem is the following, I uninstalled Facebook Beta and Facebook (non-beta), in fact I'm thinking the clash between having both installed may have caused the problem but it's been that way for months and didn't have a problem before. I then installed Facebook Beta only. Then I did soft reset. This fixed the battery problem immediately but I noticed my live tiles were no longer updating. So I went into Settings and disabled all background tasks, marking the ones I need to run in the background again the next time I open the app. I unpinned all the live tiles too, power cycled the phone, repinned the tiles, and made sure all the proper background tasks are enabled, and they all started updating again. Now the battery life is even better than it was to begin with before the problem started!