If 2 sites both use jquery.cdn/1.3.4/jquery.min.js, your browser should have it in the cache, or alternatively your caching proxy server would just serve you the bits it already downloaded earlier.
I don't think caching HTTP proxies are as useful any more now that most sites are using HTTPS. They can't easily cache content from origins that use TLS due to the encryption, unless you install a root certificate that allows the proxy to spoof any origin.
You could connect to the proxy via HTTP which then uses HTTPS to the origin, but then you'd get mixed content warnings (loading scripts via HTTP when the page is loaded via HTTPS).