Unable to sort view based on search index by taxonomy weight
I'm not sure if you have figured this out yet, but I found the solution to this, so I'll post it here in case anyone else comes along this page.

If you go to your search index and go to the Fields tab, you'll see at the very bottom there is text that says "Add related fields". It took a while for me to see this there, since it's kind of inconspicuous and under the form submit button. But if you click that and select your taxonomy, it will add the set of taxonomy fields to the available list of fields to index. Check "Weight", then that will be available in your view.