The main reason for getting the Transformer Prime was so that I could read my ever growing collection of PDF journal articles and ebooks some place other than the in front of my computer. Places like my rocking chair on my back porch or the comfort of my couch or bed. You know, the comfy places.
First off, glassy screen -> reflections. This shouldn't come as a surprise to anyone. Particularly glaring reflections can, for the most part, be dealt with by angling the screen without affecting readability too much. If this is something that's going to drive you crazy, you'll want to consider something else. Hasn't bothered me too much so far.
The brightness of the Prime means that the tablet should be readable in pretty much any lighting condition, from dark room the bright daylight. The brightness boost provided by IPS+ mode makes the screen on the Prime easily readable even in bright sunlight, although you'll pay for it in battery life. I haven't used it much for reading in sunlight too much, but it works.
The weight isn't much more than a hefty book, but heavier than your typical paperback. Holding it for extended periods of reading isn't too great a strain and so far I haven't found it terribly uncomfortable. I find for reading, holding the Prime in portrait orientation is most comfortable.
Perhaps the biggest problem I'm having with the Prime as a reader is that it's too easy to bounce around and do other things like surf the web, check mail when a new message notification pops up or check Facebook, or play a game. If you have a brain with somewhat ADD tendencies like mine, this can be a bit of a problem, especially if you're reading something that isn't quite engrossing enough to override those tendencies. With dedicated e-book readers like the Kindle or Nook, all you can do is, well, read so there isn't the temptation to bounce around to or get distracted by other things. If your brain isn't like that, then probably won't be an issue.
All in all, I'm liking the Prime for reading. I think it will rank up there as one of the better purchases I've made.