My older son did his science project on weight placement, and it worked really well. Here's a picture of the car we used:
Very simple, really. We drilled holes for one side and used slots for the other, just so the wheels were equally distant from the end of the block. The holes drilled in the top were all centered, and the proper size for tungsten 1/2 ounce cylinders. We raced the car without weights, with weights in the front, and with weights in the rear.
The same style of car could be used to check variances in weight. In fact I'm going to drill extra holes in this block and use it for that the next time our track is set up. Both of these ideas are really simple, but will have obvious results.
Another experiment I was going to try would be to see how much impact the frontal area has on speed. I was going to slice a 1/4" off of the top of a block, and then attach it on the front with a hinge. I would have a series of holes drilled through the center of the block (much like the car shown above) but in this case it would be positions for a dowel (peg). The first race would be flat, and for each subsequent trial I would raise the top part up and rest it on the peg. As the peg moves forward, the top slice would rise up more and more. The idea would be to see how much impact wind resistance has. There is also a slight weight variance as the peg moves forward, and I haven't quite figured out how to address than other than to try to make the peg as light weight as possible compared to the rest of the car weight. Basically make it "good enough" for a kid science project even if it's not super precise.
I haven't run this one, so I can't see if the difference would be significant enough to be measurable.