Your site's not able to be cached by Varnish, which is causing everything to hit your server (and not the cache), which makes you run out of memory, which makes Varnish die while trying to cache....
You're setting a PHPSESSID cookie. This makes Varnish not deliver cached pages.
The "Age" header is set to less than 1, which means Varnish is not actually serving the content for that url from cache.
Something is setting the header Cache-Control to 'no-cache' which means visitors will never get cached pages.
Something is setting the header Pragma to 'no-cache' which means visitors will never get cached pages.
Looking at your site, I think it's the wiziapp-create-your-own-native-iphone-app plugin.