It's a writing inconsistency. The only time I'm aware of where a Terminator's weight has been directly addressed in the movies is after the fight at Emery Animal Hospital in T3 between the T-850 and T-X. Here's a tongue-in-cheek running commentary of the T-850s weight discrepancy between movies.
While the T-850 fires at the T-X ineffectively, the right arm of the T-X undergoes a painfully slow transformation into its most powerful weapon--a plasma cannon capable of causing minor inconvenience to Terminators. Like the T-X, the T-850 doesn't have any basic dodge routines, so the T-X has no problems hitting the T-850 with the cannon. The impact sends the T-850 flying all the way across the parking lot and into a building. The shot also causes the sort of cartoon-styled electrical interference that acts like a temporary x-ray.
The T-850 is temporarily stunned, so the T-X converts the cannon back into a normal arm.
As John Connor flees, emergency responders are seen travelling the opposite direction. They arrive at the scene of the explosion, and EMT's quickly locate the T-850. Discovering that the T-850 has no pulse, one of the EMT's attempts to move the T-850 while the other stands there doing nothing. The EMT is unable to move the T-850, because "this guy weighs a ton". Of course. Terminators need to blend in with humans, so naturally they should be built so heavy that they can shatter asphalt and concrete on impact, and react like a stone statue when manipulated by humans. Contrast this with T2, where a 10-year-old boy was able to help a Terminator to its feet.