I'm more of a scorpion person, but I do have limited knowledge with spiders/tarantulas and I do know lots of people familiar with spiders/tarantulas. Though nobody will be up at this time spiders do that for a number of reasons.

Sometimes they clean themselves.
Other times it's simple movements like that which attract potential prey.
Also it could be a little threat display, or a warning sign.

I'm sure they have other reasons which I can't think of because I'm just getting off work and I'm tired.