Where are filter weights and settings stored other than the filter table?

I doubt this is a bug because it's bad enough that someone else would have reported it by now and I haven't found anything by searching. I probably broke something accidentally but I'm really just looking for a workaround at this point.

When I make changes on a format form eg /admin/config/content/formats/plain_text and hit the submit button, I get a message that says the format has been updated. However, the old format information shows on the form. Also, when I look directly at the filter table, the values have not changed there.

I've cleared caches repeatedly and checked that the cache_filter table is completely empty. The cache table is likewise empty.

And here is the maddening part: if I go into the filter table and manually change the weight, then go back to /admin/config/content/formats/plain_text the weight has not changed. Where is the information coming from if not from the filter table? I've looked in the variable table as well.

I'd really rather not scrap all the work I've done on the site and start over from scratch. Can someone tell me where filter weights are stored other than the filter table?