Don't worry about bulking up. Women generally have a very low amount of testosterone in their bodies, and this hormone is what causes the body to create large muscles.
What you should do is not just about weights. Cardio is vital too! And yes, I would agree that using a lighter weight and increasing reps will give your muscles a tone/lean look. As for what weight and how many reps? A simple guide would to aim for 15-20 reps, and a weight that you would end up struggling at the last 2 reps. Do note that FORM is of extreme importance when you do upper body strength workouts - you don't want to tear a ligament or twist anything!
To get really nice arms, you need to hit the Bicep, Tricep and Shoulders.
Biceps: Bicep curls using a bar. Just stand hip-distance apart and curl the bar up to chest level whilst keeping your elbows STUCK at the side of your body.
Triceps: Tricep Pushdowns using a cable. Stand hip-distance apart and push the bar down till you feel a squeeze in your muscles. Keep elbows stuck at the side of your body!
Shoulders: Dumbbell Presses. Sit on a bench with the back up. Have your arms 90 degrees while seated and press them upwards till your arms are straight up. Keep your lower back pressed against the back of the bench to prevent lower back injury. You'll be able to feel the squeeze in your shoulders.
You can do all 3 exercises as a circuit. Take a 30second rest between each exercise. Hit about 3 - 4 sets of this circuit.
If you find that hard, closed-arm push ups work really well. You can amp up the intensity with using a Bosu ball as well. Really works the core too!
As for cardio, I've found that HIIT (High Intensity Interval Training) really strips fat away, but keep it to 2 - 3 times a week or you get too ripped - something you don't want!
Hope this helps!