I didn't really notice much in the way of weight.
But, one way to possibly tell if it is a new screen where the problem shouldn't occur. Gently grab the left edge of the screen, with your thumb on the front, and 4 fingers on the back. Do this near the middle. Gently push in with your 4 fingers, and see if the LCD does the distortion effect that occurs when you touch it on the front. If it does, that is a pressure point in the screen that will probably cause them to come back. Mine did this right in the area of a white spot, if pressure was applied around the area.
If nothing shows up, then you seem to have a newer screen similar to the one installed on my Powerbook yesterday. I'm the 10th owner to have his screen replaced at the local repair center, and so far, none of the other people have said the spots are coming back.