The question you didn't think to add was; How do I get better at this? and the answer is by sight-reading every day. Find something that you are unfamiliar with, which is well below the level of pieces you're learning. It often serves to bring out the old method books that you used as a beginner, since you've probably been out of them long enough to have forgotten how to play most pieces in them. Just do a little of this each day. If you make it easy enough for yourself, you'll find yourself doing a few things naturally; the most important one is reading music in chunks, as you do with text, and reading these chunks ahead of actually playing them. Anytime I read from a score, I have temporarily memorized some small chunk of music that I'm playing, and my eyes and mind are working on repeating this process for the next chunk.
The second thing that should start to happen, without which the first doesn't really work, is getting a sense for what things on a staff will sound like or what they will feel like when they're played. If you've ever substituted an obvious word because it was part of a well-known phrase, and you just assumed it was that word when comprehending the 'chunk' of text you looked at, you know this feeling. Music has many parallels to language, and in the same way as language it has a syntax and rhythm (in a different sense than the obvious one) that one becomes familiar with. You learn to anticipate what might be coming, and you learn to deal with common patterns (scales, arpeggios, parallel intervals, broken octaves/intervals, alberti bass etc.) The best way to build this familiarity is, again, through a lot of sight-reading and wide exposure to piano literature. The importance of sight-reading for proficiency at the keyboard cannot be overstated.