Q: "I'm stronger on one side than I am on the the other. Should I do more weight on my weak side to compensate?"
A: Not usually. However, if you notice VERY large differences in development or strength, it might be a good idea to get checked out by a medical professional. There could be potentially serious underlying reasons for severe muscular imbalances (disease, nerve damage, injury, etc.). Once cleared by your med pro, consider the following:
1 - Sometimes we develop imbalances due to form faults (cheats), or lack of experience on a particular movement. Have a friend or trainer (we know some good ones) watch you do movements where you notice the most weakness occurring. Maybe, another set of eyes will see these form faults and show you where you can make improvements.
2 - Weight machines are notorious for contributing to weak-side imbalances. Weight machines give you very little feedback in terms of knowing whether or not you are pushing harder on one side vs. the other. If you are working out with weight stacks to the exclusion of BBs and DBs, you have almost surely developed imbalances. Not to mention a very poor quality of fitness devoid of functionality (HA! But, that is a subject for another post).
3 - Prior injuries you've suffered may contribute to a lack of flexibility in certain joints. This lack of flexibility may cause strong-side compensations. Again, another set of eyes can help you discover this. Have someone watch to make sure you aren't shorting the ROM (range of motion) on a particular side, or leaning away from an old injury. If you are, it will be well to consult an expert to help you learn stretches to improve your functional flexibility.
We are all naturally strong sided (right, or left handed). Our dominant side usually dictates strength and development. It is perfectly natural to be SLIGHTLY stronger/more developed on one side vs. another.
When it comes to getting the most out of your workouts, balance is key. Creating deliberate imbalances by going heavier on your slightly weaker side is more likely to mess things up, than it is to help.