Running with hand weights or weight gloves are a great way to develop shoulder problems. Remember, your shoulder joint is nothing more than a bunch of tendons and ligaments...it is not a true ball and socket joint. View your arm as a pendulum attached to the top by a string. If you put a large weight at the end of the pendulum it will eventually break the string.
Ask yourself this question: What is the arm action during the running stride? Are you repeatedly flexing your arm like arm curls? Or...are you repeatedly moving your upper arm back and forth while your elbow generally maintains a 90 degree angle? Your answer would be the latter.
So, which muscles are responsbile for this back and forth motion and how do you strengthen them? That should be your goal. The muscles responsible would be mostly the anterior deltoid and posterior deltoid (ie: shoulders) and your latisimus dorsi. The clavicular portion of the pectoralis muscle (upper chest) is also engaged somewhat.
A general upper body workout for a runner would look something like this:
Bench Press
Dumbell Pullover
Front Raise
Seated Row
A more "running specific" upper body workout for a runner would look something like this:
Standing Single Arm Cable Row
(Also, same as above but rowing while standing on one leg, the other leg extending out in front like a running motion)
Standing Single Bent Arm Front Raise (ie: Arm Drive)
Reverse Lunge w/Single Arm Cable Row (Row on the way up, knee drive on the way up, ie: like an exaggerated running motion)
Bent Arm Cable Push Pull
Alan