The PID coefficients in a feedback control loop are tuned to work for that specific system. So, if any changes are made to that system, like increasing the speed in your line following robot, the PID coefficients will likely need to be tuned again. The coefficients should be easier to tune with smaller changes. So, your tuning process should be: start with the line following code that you know works well, increase the speed by a small amount (e.g. if your robot is working well with a default speed of 50, try using a value of 53 or 55, as opposed to trying a much larger value like 75 or 80), observe the behavior of your robot as it follows the line, make a small adjustment to your coefficients based on the performance, and test the robot on the line following course again. Once you get your robot following the line as perfectly as you can at the current speed, then you can try increasing the speed again by a small amount and repeating the tuning process.
By the way, since your robot is following the line okay without KD (i.e. KD currently has a value of zero), it looks like your PID controller is probably ready to use a derivative term to make it follow the line even more smoothly before starting to increase speed. You can get a good idea of how to start adding KD to your controller by reading this post by Ben.
-Jon