Hydration — It's all personal, but when I'm doing long and fast miles, a hydration pack gets in the way. It's a pain to take it out and refill it, and I think that psychologically-speaking, it can lead to carrying more water weight so you have to stop less. With a wide-mouthed Gatorade bottle and micropur tabs, it's a 60 second process (max) to lean over, dip it in a stream, and fill it up.
If I'm only going to be out for 2-4 hours, I'll bring the hydration pack.
Tarp – I also use a Polycro groundsheet. Weighs 1.5 oz or so. I bought a two pack for cheap from Gossamer Gear, but you can also buy window insulation film and that's basically the same stuff. That combined with a headnet will keep you plenty comfortable.
I use a Tarptent Cloudburst 2 when I go out with my wife because she hasn't quite bought into the tarp thing. The Cloudburst is great, though. Super roomy, built in floor and bug net. But the trade-off is that it weighs 37 oz. Not a big deal when you're doing 15 miles or less per day, but when you're running, it makes a difference.
Pad – Get the short-sized Gossamer Gear Nightlight. I have a Ridge Rest which I like, but I think the Nightlight would be the way to go if I had to do it again.

