My access log says that the jetpack scripts are being loaded from my server. Is there some kind of option I can tick to make sure they are being served by wordpress.com?
Jetpack doesn't offer any option to host these resources for you. The Photon module allows you to serve all images from the WordPress.com cloud, but that only applies to images.
My website is using the most resources from my shared host and I'm in danger of having my site shut down if I don't reduce the resource load.
You can use a Content Delivery Network (CDN) to offload the bulk of your javascript libraries and other static files to another server. I don't use any CDN myself, so I can't recommend any specific one, but I'm sure you could find helpful posts and recommendations here in the support forums.