I have seen a couple posts that sound like my problem, but no real answer I can find. I am using Weaver Xtreme (latest… along with latest everything else). On my page with posts, I get 2 Continue Reading links. I tried disabling all plugins except for the Weaver Xtreme, and it still happens. One such page is: https://spray-lining.net/aeonxcoatings/articles/
Do make 100% sure you tested with ALL non weaver plugins disabled.
Are you using a child theme? If so try without it in case something in the child needs to be updated.
If you create a test page based on the page with posts, with all default options, do you have the same issue
If you have the weaver Show posts plugin installed, try creating a test page based on the default template, and add the posts using a weaver show posts shortcode (after you create a show posts filter), and see if the same problem appears there.