>I have the hardest time trying to up my weights without total
>fatigue.
Actually, "total fatigue" is what you're looking for is you want to increase strength. If you do a workout that fatigues the muscle, the muscle will rebuild stronger (if givne enough recovery in the form of nutrition and time off from working that muscle).
You can increase bicep strength by doing negative reps (not too often, they are very tiring). On the last set of bicep concentration curls (once a week), use a bit heavier weight than you would usually (ie: if you use 10#, go to 12#, Platemates, as others have mentioned, are great for this, and for increasing weight in general in a more doable increment). Do as many as you can with good form, then when you can no longer do a positive rep, use your opposite hand to help you get the weight into position, then lower with control under your own power. Do 3 or 4 of these "assisted, negative reps."