Should I have thicker areas of foundation under posts?
At a 3000psf bearing capacity of the soil underneath, each 8x8 post without footing can bear a paltry  27 sqft at 50psf live load.
(3000psf x 64 sq-in / 144 / 50psf) = 27 sqft
If this is all you need, you still have to worry about post tilt due to an uneven bearing capacity or hardness gradient under such a small post.
You need a soil analysis and a load calculation by a structural engineer.