You read by requesting the relay find information and send it to you, according to some filter. (Filters are boolean, unlike queries, so they tend to be cached after use for better performance when re-requested, but I digress.)

So, the cost is in filtering and returning the result, and possibly in caching the filter.

You can overwhelm a relay by requesting lots and lots of filters or lots of npubs requesting something be filtered.

AUTHing to read means that you have to identify yourself to the relay, and be approved, before it runs a filter.

I think. Maybe. Just guessing. Don't really know. Ask someone with more clue. HTH.