With how sad steps, O Moon, thou climb'st the skies! How silently, and with how wan a face! (1-2)
Right from the start, we get sadness. "Sad steps," "silently," and "wan." Sure, "silently" and "wan" can mean other things, but the image is of somebody sulking upstairs to their room with their head hanging down.
Sure, if that long with love-acquainted eyes Can judge of love, thou feel'st a lover's case; (5-6)
A "lover's case," eh? Why not just call it what it is, Astrophel: downright sadness, depression, and frustration. Wait, what about joy? Nope, the "lover's case" (i.e., the lover's situation) in this poem is all about those negative emotions. It's kind of unfair, but hey we didn't write it.
I read it in thy looks; thy languisht grace To me that feel the like, thy state descries. (7-8)
It's easy to tell when somebody's sad. It's as simple as looking at somebody's "looks" and "reading" them, as if they were a book. Sure, it helps to be feeling the same thing, but that's no bother.