Well I think Mr Witt nailed it. The tattoo is like the objects in the world, it touches us but is not exactly us but it becomes a part of us. So light helps us take in the world just as a spider connects this to that as if a filament of its web connects all to us and us to all.
This one has eluded me for years. Perhaps that's one reason I find it attractive.
Let me start with the title, Tattoo. A permanent design or mark on the exterior of the body, usually in the form of a drawing or image. Body art. (Bear in mind that Stevens is writing during a period when tattoos were not in vogue as they are today in 2006. There was something forbidden about them; something exotic and intimidating, but also a little debasing. They were reserved for sailors, criminals, and aboriginal tribesmen.)
But Stevens doesn't talk about that. Instead, he sets to work with light, like a spider, crawling, and spinning a web. The light crawls over the water, and over the edge of the snow (a hearty spider, to be sure) . It's an image that, so far anyway, makes sense.
The spider (light) spins its web under the reader's eyelids. (Around this time, some fashionable women would have their eyeliner tattooed on. Could that be what he's referring to? A fashion statement? I doubt it.) So the light makes a discernible pattern under your eyelids, and spreads its webs there-its two webs (one for each eye) . Well, okay. I've experienced that, closing my eyes and facing the sun to feel its heat and enjoy the diffusion of light through my lids. Yeah, so far so good.
But maybe Stevens is talking about more than that here. We all close our eyes to remember something, or to visualize something that is not immediately before us. As if our memories are patterns indelibly drawn on the inside of our eyelids. (Perhaps we're getting somewhere here.)
These webs, the webs of your eyes, are fastened to the flesh and bones of you as to rafters or grass. So the webs of light become part of you, they fasten to you. What you see, what you witness, becomes part of you. There is an indelible pattern etched upon your body-or more precisely your brain-by all that you see, all that you perceive. You are marked by these webs that light spins. You cannot see without being changed, and permanently.
But then, there are also filaments of your eyes on the surface of the water and in the edges of the snow. When you see, you change or at least affect the object that you see. (It's almost a scientific viewpoint: the observer changes the observed merely by the process of observing. Ask any physicist.)
So the tattoo or marking works both ways. The seeing marks us, and we by seeing mark what we see. The light weaves its web upon us, as upon rafters or grass, and we leave filaments of our eyes on the surface of the water and in the edges of the snow.
I'm afraid that's the best I can do on this one. Stevens was a hell of a lot smarter than I.