Tim Bray answers a question asked by James Governor: "IS AJAX expensive?". Tim is correct - the question, as asked, is unanswerable. A CSS reference could conceivably be expensive, if the resulting CSS is huge. Heck, a bunch of image references could be expensive, depending on how they are retrieved (static files, blob lookups in a database, dynamic image generation - you get the idea).
In and of itself, AJAX is simply a way of making asynchronous requests. Whether those requests are cheap or expensive is a separate - and unrelated - matter.