I do a run every day while being pulled to my impending doom by two large hounds who's idea of exercise is to see how fast they can go while chasing suburban game when dragging the weight of a human behind them. It makes for a great cardio workout sometimes. Usual distance is 1 to 2 miles with lots of stops, starts and bursts.
I've tried lots of things to carry stuff with me (including water for the dogs) while this is going on and in the end the only thing that I have found which works is to get a small thin backpack such as the CamelbaK one
It HAS to have two shoulder straps, a waist band and a chest tightening band.
Once put on and secured, I find it pretty easy to carry several pounds of weight without a problem during a mix of walking, stopping, jogging, running, sprinting, trying to move your legs fast enough to not die.
What does NOT work at all is the single strap sling type... those are the worst.
The important features are dual shoulder straps, the strap to tighten up at your chest and the strap to tighten up at either waist or lower stomach level.