Symbolism, Imagery, Allegory
This is kind of an obvious one. In a book about an Invisible Man, there's going to be a lot of time spent on what people can and can't see.
But it's not that easy. There are also plenty of times in The Invisible Man where sight is used metaphorically. For instance, the Invisible Man notes that, when he developed his formula, he had a "vision of all that invisibility might mean" (19.38).
Something tells us that Wells used that word – vision – on purpose. Here, sight represents the ability to see the future. So what does that mean when someone is invisible? Maybe not being able to see the Invisible Man (literally) might be linked to not being able to see the future (figuratively). For Wells, the future meant science, and lots of it.
Focusing on sight – or the lack thereof – may remind us how little we really understand about the world and the future.