The last Weaver scene has a pretty difficult interpersonal insight check (270 IIRC) that you need to pass in order to unlock the Weaver secret and ally with Avalie. You’ll also need high persuasion to convince her, but I don’t think it’s higher than 500 (which you’ll need anyways to convince the Jiyel ambassador for the legendary ending).
It's actually 275, and even MCs that specialize in people/politics knowledge would need to grind a bit to get there!
Considering how busy you can get trying to get the secrets to the legendary endings, I definitely recommend getting the practice in earlier than week 6. I ended up 5 points short of it myself, and had to load up a save two weeks earlier because I didn't have enough free time slots, RIP.