Nice to see a fellow Buckeye on the board!
A heavier weight for a larger muscle? Yep. The idea is that you want to present a challenge to the muscle group you are engaging. The back muscle, latissimus dorsi, runs from under the arm, across the back and down to Iliac crest of the pelvis. That is one large muscle and it is very strong. It is capable of a very heavy weight. To work this area you would need to select something much heavier than you would use to work the shoulders, deltoids. For example, when working my lats, I choose a 40 to 45lb dumb bell to do lat rows to truly engage that muscle for 10 to 12 reps. However, I would seriously injure myself and those around me if I selected a 45 dumb bell to do lateral or frontal shoulder raises at that weight.
In the beginning, select a weight that is challenging for you to complete by the 10th to 12th rep of the set. As you progress, and you find that this becomes easier then it's time to alter your workout for another challenge.
Strength goals are usually met by selecting a weight that is heavy enough to fatigue you by the 4 to 6th rep of the set. This is going to be a rather heavy weight.
Muscle endurance goals can be reached by selecting a weight that allows you to complete 12 or more reps before experiencing muscle fatigue. This is going to be a lighter weight.
A good balance between the two that will encourage both muscle growth in strength and endurance is a rep range between 8 to 12 reps. With proper nutrition, leaning out, it will also allow you to reveal nice hypertrophy of the muscle group.