I'm confused by the way the range for Target Heart Rates is labeled. 
On the treadmill I use, the range extends from "below target heart
rate" to "weight loss" to "cardiovascular training" to "above target
heart rate." Often I find that I have to hold myself back/slow down in
order to keep my target heart rate in the middle, "weight loss" range,
since my ultimate goal is to burn fat and lose weight. I worry that
even though I can comfortably jog faster, I would be increasing my
heart rate past the "weight loss" range and into the "cardio" range.
Does reaching these upper limits of the target heart rate nullify or
reverse the weight loss effects of excercise at a lower heart rate, or
does it simply add a cardiovascular benefit to the weight loss, and by
burning more calories, actually increase my weight loss potential? In
a nutshell, can I run at my full (safe) potential, or should I slow
down to lose more weight?

Good question. The short answer is that you will actually lose more
weight by running faster. A common misconception stems from the
following facts: the proportion of fat burned substantially increases
after 10 minutes of excercise. After about twenty minutes of
excercise, 80-90% of your energy comes from burning fat. (You should
maintain 60-90% of your maximal heart rate while excercising; your
maximal heart rate is 220 minus your age in years). So, people think
that if you are doing strenuous excercise, e.g., something like the
800m, which takes less than two minutes for athletes, that it will
burn mostly sugar, not fat. This is true for the duration of the race.
However, after the strenuous excercise, the metabolism of fat will
also be increased. In fact, the majority of our energy used while
sitting in front of this computer, walking around, etc., is from fat,
not sugar. Therefore, if you run for 10-20 minutes or more, you will
definitely burn more fat by running faster and getting winded. If you
jog slowly for the same amount of time, the percentage of your energy
that comes from fat will be increased, but it will not be more fat
burned overall.

Actually, purkinje's answer is not quite accurate. While it is true
that you will burn more CALORIES working out harder with a faster
heart rate, it is not the case that you will burn more fat. When the
heart rate increses to the "cardiovascular range," you are burning far
more carbohyrates than fat. Carbs are actually a very good source of
energy for the body and they break down easily into glucose which
feeds the brain. Since fat does not provide sufficient energy to the
body, when you increase your heart rate too much, carbohydrates become
the primary fuel. Again, this will lead to more calories being burned,
but you will burn less fat. This is particularly a problem if you are
on a low to no carb diet, because maintaining a high heart rate will
cause your body to break down muscle INSTEAD OF FAT! Since muscle
weighs more than fat, you will actually notice substantial weight
loss, but this is not the result of losing fat cells. So be very
cautious in how you choose to work out.