It looks like one possible answer is, unsurprisingly, curl
:
$ curl http://example.com/ --silent --write-out "%{size_download}\n" --output /dev/null
31032
$ curl http://example.com/ --silent -H "Accept-Encoding: gzip,deflate" --write-out "%{size_download}\n" --output /dev/null
2553
In the second case the client tells the server that it supports content encoding and you can see that the response was indeed shorter, compressed.