Anyone whose read any of the other threads on this topic know that I'm a nerd about this stuff. There are a million good reasons that lighter is better. Liability is really low on my list -- but it still matters, as it should for anyone who crosses jurisdictions (my legal Alberta rig could net me some fines in BC, for example). I don't have the energy or time to understand the minutiae of every jurisdiction's legal codes, so for me, staying within the design limits is a good practice.
Higher on my list than the legalities (as others have mentioned) is safety. A heavy rig doesn't stop as well as a light rig, regardless of what the door sticker says. And, as an Overlanders, we are WAY more likely to get into an accident in our car than we are to face some of the other risks we prepare extensively for (for example, some people refuse to buy cars with autos because they cannot be bump started. There's a 1 in 109 chance of dying in a car crash. I don't know exactly what the odds are of dying from being unable to bump start a car but...I'm going to bet it's a lot lower than 1 in 109.)
Animal strikes are common. When Bullwinkle jumps out of the ditch in front of me, I need to stop, but weight really makes that difficult because it's proportional -- a 4000 lbs object will require twice the stopping distance of a 2000 lbs object, all other things being equal. So imagine we have two trucks on the same tires and Bullwinkle is 100 feet away. The 5000 lbs truck needs 70 feet to stop. The 6700 lbs truck hits the moose (I'd suggest double checking my math...I'm really fast at math. Not accurate...just fast!). This is a simplified example but what does that look like in the real world?
The 5000 lbs truck is about 1000 lbs under GVM, and a common figure for payload of these trucks is about 1500 lbs. So thats a single person with a big dog and a backpacker's approach to camping, with basic emergency gear in our 5,000 lbs truck. For the 6700 lbs truck -- well, It doesn't take much to hit 1700 extra pounds of stuff: Bumper front and rear with winch up front (250 lbs). Skid plates (100 lbs). Big tires (25 extra lbs each with a full size spare so 125 lbs). Roof tent (150 lbs). Awning (50 lbs). Fridge (40 lbs....70lbs if you drink a lot of beer). Second battery with wiring etc. (150 lbs) -- I've just described a pretty typical build in the Overland community using relatively conservative numbers, and I'm already over 850 lbs in kit before I've even included the driver and his or her essentials, and note I've not included spare gas, water, a roof rack, the recovery kit, food, or anything like that yet. The point is it's easy to be way over weight without realizing it, because it adds up fast, and that weight is the difference between hitting the moose and not hitting it.