Ok I did not realise this. Since you are not the one who started the thread, you could not see the private message. Here is the message in full –
I was able to get the fonts working. I changed the URLs a bit. For Weston, I had to change the URL from https://www.livemeshthemes.com/extinct/wp-content/fonts/weston/… https://www.livemeshthemes.com/extinct/wp-content/fonts/Weston/…
For outage font, I had to change the font-family in the markup in the style.css. Looks like you missed changing the font-family to outagregular for heading styles in the child theme style.css even though you inserted the URLs for the font there.
I am really sorry this caused trouble for you. Obviously, in most cases like this, a single step missed will invalidate everything else. It will help others too if you can tell me the exact step I missed since we sometimes we just assume certain things.