I have been diagnosed as pre-diabetic and would like to monitor my sugar intake. What should be my daily grams of sugar per 135lbs body weight?

Count carbs. Eat like a diabetic and you'll keep from being one. Ask your doctor to send you to diabetes education class. It is usually covered for those with pre-diabetes also. "sugar" is just a simple carb, and those are bad. Complex carbs are good. A diabetes education class will help you learn to eat more healthfully, schedule food regularly, and get daily exercise.
Low glycemic diet. Instead of thinking in terms of the amount of sugar you should intake, think of ingested a low glycemic diet. There are lots of websites that tell you the glycemic index and glycemic load of foods. Eat or drink only those with low levels. Strive to pick those foods with a glycemic index of less than 60 and glycemic load of less than 15 if you can.