I'd not heard of Cartweaver before, but I've had a quick look at the documentation and skimmed a few reviews and it sounds like you'd basically need to install Cartweaver as a site within your SilverStripe site, rather than having them work together in any real way.
I'm writing this here in case anyone else wants to do the same thing, and comes across this thread.
I couldn't see any mention of an API that might mean you could, for example, display some product details from the system in a page in your SilverStripe page, although you could probably get SS to do that if it can read from Cartweaver's database. So the work would, as I understand it from a very cursory skim, basically be:
1. Tweaking your server configuration (if Apache, it would be .htaccess) so the appropriate URLs go to the Cartweaver site. Either as a directory within your site (eg james.com/shop) or on a separate domain (eg shop.james.com).
2. Doing what you can to match the site design, based on the theme you're using in SilverStripe.
I might be totally wrong about this of course, as I have no experience with Cartweaver.
Feel free to get in touch if you're still interested in help (perhaps someone else will respond to you too!).
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