Dart thinkness depends and the material you use. 1/2" is good for a nice heavy dart, but 3/8" might very well be perfect. Many material taper too, and many of the principles applicable to arrows apply. Diameter for me is just a guild. Spine is more important. You probably will not know your ideal spine with until you toss a few, because it is a function of the power of your toss, arm, stance, leverage, etc., but 5-7 lbs is recommended. Grab one end of the dart and push the other end into a bathroom scale. It will bow out and then at some point, stop increasing in weight, even if you push more.
Atlatl and dart length will vary with the user. Most say that the lenght from your elbow to finger tips is ideal for an atlatl. I can only say that that works for me, but a short one I made, 16" is difficult for me to use. Some like 7' darts others 5', even less or more. Of course length affects spine, which to me is more important.
On weight, I have heard that if they are about the same that is good, but I don't know. I do know that I like the feel of an atlatl with a stone weight added. My darts are mostly 4-6 oz, which I have heard is heavy. I have heard of those that are heavier, but I have also heard, been recommended, and seen more of those that are 1-2 oz.
Experiment and have fun.