I've had a similar problem. I hypothesized that weak arms were easily fatigued when the legs drew in energy need for powerful strides. Simple bicep curls and exercises should do the trick. Working on triceps at the same time doesn't hurt either.
I devised a rudimentary yet effective weight plan.
Week 1 - 3 workouts of 4x5 bicep lifts at Weight #1.
Week 2 - 3 workouts at 4 x 8 bicep lifts at same weight.
Week 3 - 3 workouts at 4 x 12.
Week 4 - 3 workouts at 4 x 15.
Week 5 - 3 workouts at 4 x 18.
Week 6 - 3 workouts at 4 x 20.
Week 7 - 3 workouts at 4 x 5. Increase weight by five pounds. Do the same as the last six weeks except with the increase of weight.
Every six weeks increase weight by five pounds.
Very gradual, very rudimentary, but you don't need much when strengthening presumably weak biceps. You can do the same thing for your triceps with specific triceps workouts.