Are they looting the body? Reanimating the dead? Stealing his last glimpse of vital aura? Performing pranotherapy? I have this guard in Morthal who just doesn't stop doing this weird thing over a dead spider, every time I'm passing through I'm like wtf man, aren't you finished yet?

Checking to make sure it's dead, I'd say. You'll often hear them say things such as "I'm going to find whoever did this." when checking the body of a dead NPC. Perhaps they want to make sure the spider is really dead?

Haha I thought they were mourning the dead but I never saw them do this to spiders, could be looting after all. But in that case it's robbing the dead which is not cool for a priest I saw doing this