To be able to run with any pack, but especially a heavier overnight one, you have to have a comfortable pack. Comfort when it comes to running with a pack is principally about minimizing pack bounce. Pack bounce is minimized when weight is transferred substantially to your hips with shoulder straps being used primarily for load stabilization. Small, short packs, typified by hydration-style packs, tend to transfer weight only to your shoulders. Even with a very light kit, repeatedly weighting your shoulders while running tires them quickly. A pack sized appropriately for your torso allows proper weight distribution. You should be able to cinch your pack down to the size of its contents to keep the contents from bouncing within the pack. A pack with easy access to food and water saves significant time while traveling and encourages eating and drinking regularly throughout the day. My personal favorite is the 2,100 cubic inch ULA Relay. Its waistbelt pockets and three hydration options (bladder port, shoulder strap bottle holders, and side water bottle holders) make getting calories and fluids easy. Packs should also allow unobstructed arm swings. The appropriate size will vary with your kit, but even with an internal hydration system and sleeping pad, 2,100-2,800 cubic inches should work for most users. If you bring a minimalist pad or attach it to the outside of your pack, you can subtract 500 to 700 cubic inches from these numbers.
If you're pretty sure you can improvise a soft sleeping spot, and it's not predicted to get very cold, you can get by with a thin, body-sized pad. If the weather contains no chance of precipitation (this is easier to predict with certainty for two-day trips and much less certain the longer you're out) you may be able to leave a tarp and bivy sack behind. On longer trips where you "probably" won't need rain protection, a ponchotarp can save significant weight. However, if you end up using it, a ponchotarp makes it much more difficult to see your feet - especially important on more technical trails - which limits its utility. Running with one? Good luck!
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