I have not taken both tent and tarp. When using a bivy ot bug bivy, I do take a tarp and pitch the tarp over the bivy.
Oh, and since ground sheets were mentioned ... I do not use a ground sheet. I found over the years that I am better off to just patch and holes in the tent bottom and recoat it if it ever gets that bad. I figure that eventually I could use a plastic sheet inside the tent if the floor ever really wears out. It could be a bit oversize so it wraps up the sides just a bit. The thing is that even without a ground sheet something else wears out or fails first any way. It may be because crawl into the tent onto the sleeping pad kicking my shoes off on the way in and lay right down. I pretty much am either reading or sleeping when in the tent so I don't put much wear and tear on tent floors.