As I understand it weight, in and of itself, doesn't count for a whole lot and doesn't correlate directly to increased safety. It can help determine how much damage your vehicle will do but it has little influence on the safety of the occupants.
Weight, in and of itself, doesn't impact safety. This is true, in that, if you crash a light vehicle into a wall and you crash a heavy vehicle into a wall, as long as they are designed properly to pass that particular test, both should be able to sustain the impact with minimal passenger compartment intrusion. This is how most crash tests are done...they run the car into a static object and measure the G-forces that are imparted on the passengers and the level of passenger compartment intrusion.
Where weight does have an impact is when you crash a heavier object into a lighter object. (Say a truck into a car). The heavier object will typically continue on its original path, whereas the lighter vehicle will be forced to change direction quickly. Depending on the weight disparity, this direction change can be sudden and violent. Often more violent than crashing into a static wall. Especially since speed is cumulative (take two cars heading 30mph, crash them into each other, you now have essentially the same crash as one car running into something at 60 mph).
While crash testing has gotten better, both the NHTSA and the IIHS say their front and rear crash tests are only comparable against vehicles of the same weight class. Their side crash tests is done with a moving chassis that represents the height and weight of a midsize SUV (like a Ford Explorer), but even that isn't perfect...as a midsize SUV is a smaller and lighter vehicle than a full size pickup or SUV.
You also brought up the other issue, height. The higher ground clearance of suvs and trucks also leads to a disparity in crashes between smaller cars and larger trucks/suvs. This height difference combined with the weight difference can turn even a low speed crash into a real problem for the smaller lower car.
Height is a bit of a double edged sword though, as the higher a vehicle is, the greater potential there is for roll-over incidents. Thankfully, traction/stability control, airbags, better tires, and tougher roof-crush standards have made rollover incidents significantly more avoidable and survivable. It's still something that drivers need to be aware of though.
In fact, that is why my Suburban is no longer one of my daily drivers. While it's a heavy and high SUV, being from 1995 it lacks such features as side airbags, stability control, traction control, high strength steel, a more crush resistant roof, ect. I've been planning to buy a newer model full size SUV to replace it, however I prefer diesel engines and have been waiting patiently for one U.S. manufacturer to release a diesel full-size SUV. Unfortunately, no one has yet (even though GM has been teasing me with concept versions for years).