The skeleton app with just the core Meteor packages weighs in at 101KB (look at http://testskel.meteor.com/ in the Chrome network analyzer), which is not too bad. However, since all of your app code is loaded at once on the first load, if you’re not careful it’s easy to inflate the size. On the other hand, after the initial load of all of the app code the only other network traffic is the data sent over the wire. This should be a lot less than the HTML that would be sent in a “normal” AJAX or server-side rendered app.
You can use the
appcache package to make your app available for use offline (of course, without the data). For a demonstration, check out https://docs.meteor.com (turn off your internet and visit the page again!).
There are also some community packages like GroundDB that will help you store data offline if you need to.
What devices are you targeting? Desktop or mobile?