How thick a piece of canvas is affects how strong and heavy it is. 12 oz. is much heavier than 8 oz., and that extra "mass" will make it a little stronger. But the primary feature affecting its abilities to repel water is how TIGHT OF WEAVE it is. The tighter the threads are woven together, the less room for water to come through. And when that fabric gets wet, it swells up closing those gaps even farther. Paints, oils, and chemicals used to "waterproof" fabric soak into the threads, swelling them up - thus closing the tiny holes in the finished fabric. And some of the stuff added on also sticks to the outside of the material - also filling in those tiny holes.
How strong of initial fabric you would want depends upon how you are going to use your trail tarp, and how long you want it to last. If you are going to hump it through the woods a lot, weight means a lot. So then you go with a much lighter fabric, knowing that it will not be quite as strong and not last as long as the heavy tarps. If you are always setting up at drive-in events where you don't have to carry it much, then the thicker material will give you longer life, a stronger fabric, hold up better in strong winds, and just look more substantial. The trade-offs are there.
There are a number of people that have purchased very high quality thread count linen sheets to make their trail tarps - 400 to 600 thread count or higher. These work well to repel water, even without any waterproofing "treatment", but some does help. And their trail tarp is very light, and roll/pack up very small. Now, those sheets are not as strong as 12 oz. canvas, but the trade-off in weight and initial cost was well worth it.
Sewing Loops on a tarp is a fairly modern practice. It also creates a stress point in the fabric, and can be one of the first places to tear out. A much more appropriate option is to tie a small pebble or roundball into the corners of your fabric, using some light cord/rope - and anywhere else that you want a tie point. These spread the stress of the tie-point around much better, and are easy to remove, replace, or move (unless your knots are a tad too tight).
I've used a 9x12 painters tarp from SWP for years, with those roundball ties in appropriate places. I set it up a lot as a diamond fly (9x9 with 3 feet tucked under), and in quite a few other configurations. It's about a 10 oz., and a tad heavy to carry far. I've also sewn up a 6 x 7 1/2 by 6 feet high wedge tent out of 8 oz. that weighs about the same. Now I'm looking for some 6 oz. fabric for a new trail tarp - if it's of tight enough weave. So goes life.
Of course, these are buy my humble opinions, and best used in conjunction with your own research.
yhs
Mike Ameling