Ill drop my 2 cents:
Yes it is bad for FPS. In general, you have two types of aiming: Pinpoint+high sensitivity (using your wrist and fingers mostly for moving the mouse), and low sensitivity (where you will use the arm mostly).
Now, depending on what fps you are playing, you might favor one type or the other, but one thing will still be true:
If the mice is heavy (I dont mean it has to be as light as possible, but not too heavy) and you use the fingers+wrist to move the mouse, the inertia of the mice is going to make you overshoot your target. This means, you will have to make counter force to compensate for the movement.
Now that is not good. The second situation is that you will be moving with your arm a heavier mouse, meaning your arm will have less precision (the more force we use, the less precise it is). This is important because if you try to keep the precision at the same level, more muscles are going to be constantly stressed in your arm.
I have been puzzled by what would be *the perfect mouse* for years, and I came to the conclusion that as long as it stays in certain parameters, they dont matter that much (since its mostly about getting use to it thru practice).